LMFDB - Embedded newform 357.2.bl.a.250.9

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			250.9
Character	$\chi$	$=$	357.250
Dual form			357.2.bl.a.10.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.870777 - 0.114640i) q^{2} +(-0.442289 + 0.896873i) q^{3} +(-1.18674 - 0.317986i) q^{4} +(3.24146 + 2.84269i) q^{5} +(0.487952 - 0.730272i) q^{6} +(-2.13834 + 1.55805i) q^{7} +(2.61980 + 1.08516i) q^{8} +(-0.608761 - 0.793353i) q^{9} +(-2.49670 - 2.84695i) q^{10} +(-2.31301 - 0.151603i) q^{11} +(0.810076 - 0.923714i) q^{12} +(1.06136 - 1.06136i) q^{13} +(2.04063 - 1.11157i) q^{14} +(-3.98319 + 1.64989i) q^{15} +(-0.0288541 - 0.0166589i) q^{16} +(-3.25106 - 2.53587i) q^{17} +(0.439145 + 0.760622i) q^{18} +(-0.579980 + 4.40539i) q^{19} +(-2.94284 - 4.40428i) q^{20} +(-0.451605 - 2.60692i) q^{21} +(1.99674 + 0.397175i) q^{22} +(-1.83737 + 0.906089i) q^{23} +(-2.13196 + 1.86968i) q^{24} +(1.77358 + 13.4717i) q^{25} +(-1.04588 + 0.802535i) q^{26} +(0.980785 - 0.195090i) q^{27} +(3.03309 - 1.16903i) q^{28} +(-0.649389 + 3.26470i) q^{29} +(3.65761 - 0.980054i) q^{30} +(-5.19406 - 2.56143i) q^{31} +(-4.47614 - 3.43466i) q^{32} +(1.15899 - 2.00742i) q^{33} +(2.54024 + 2.58087i) q^{34} +(-11.3604 - 1.02828i) q^{35} +(0.470167 + 1.13508i) q^{36} +(0.361233 + 5.51135i) q^{37} +(1.01007 - 3.76962i) q^{38} +(0.482478 + 1.42134i) q^{39} +(5.40723 + 10.9648i) q^{40} +(0.575032 + 2.89088i) q^{41} +(0.0943899 + 2.32182i) q^{42} +(-3.01755 + 7.28500i) q^{43} +(2.69674 + 0.915419i) q^{44} +(0.281977 - 4.30214i) q^{45} +(1.70381 - 0.578366i) q^{46} +(-0.997470 - 3.72261i) q^{47} +(0.0277028 - 0.0185104i) q^{48} +(2.14499 - 6.66326i) q^{49} -11.9342i q^{50} +(3.71226 - 1.79420i) q^{51} +(-1.59706 + 0.922064i) q^{52} +(6.82093 - 8.88921i) q^{53} +(-0.876410 + 0.0574430i) q^{54} +(-7.06658 - 7.06658i) q^{55} +(-7.29275 + 1.76134i) q^{56} +(-3.69455 - 2.46862i) q^{57} +(0.939738 - 2.76838i) q^{58} +(7.24418 - 0.953715i) q^{59} +(5.25166 - 0.691394i) q^{60} +(-0.451353 + 1.32964i) q^{61} +(4.22923 + 2.82588i) q^{62} +(2.53782 + 0.747980i) q^{63} +(3.55108 + 3.55108i) q^{64} +(6.45749 - 0.423246i) q^{65} +(-1.23935 + 1.61515i) q^{66} +(11.8097 - 6.81835i) q^{67} +(3.05180 + 4.04321i) q^{68} -2.04864i q^{69} +(9.77447 + 2.19776i) q^{70} +(-10.2549 + 6.85214i) q^{71} +(-0.733921 - 2.73903i) q^{72} +(2.27983 - 0.773899i) q^{73} +(0.317267 - 4.84056i) q^{74} +(-12.8668 - 4.36770i) q^{75} +(2.08914 - 5.04363i) q^{76} +(5.18220 - 3.27960i) q^{77} +(-0.257189 - 1.29298i) q^{78} +(6.20687 + 12.5863i) q^{79} +(-0.0461734 - 0.136022i) q^{80} +(-0.258819 + 0.965926i) q^{81} +(-0.169314 - 2.58323i) q^{82} +(0.458903 + 1.10789i) q^{83} +(-0.293028 + 3.23735i) q^{84} +(-3.32951 - 17.4617i) q^{85} +(3.46276 - 5.99768i) q^{86} +(-2.64080 - 2.02636i) q^{87} +(-5.89512 - 2.90715i) q^{88} +(5.85285 - 1.56827i) q^{89} +(-0.738737 + 3.71388i) q^{90} +(-0.615902 + 3.92320i) q^{91} +(2.46860 - 0.491036i) q^{92} +(4.59455 - 3.52552i) q^{93} +(0.441814 + 3.35591i) q^{94} +(-14.4031 + 12.6312i) q^{95} +(5.06020 - 2.49541i) q^{96} +(-3.69653 - 0.735286i) q^{97} +(-2.63168 + 5.55631i) q^{98} +(1.28780 + 1.92732i) 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 $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{16}\right)$	$1$

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 $

$2$	−0.870777	−	0.114640i	−0.615732	−	0.0810627i	−0.183792	−	0.982965i	$-0.558837\pi$
$2$	−0.870777	−	0.114640i	−0.615732	−	0.0810627i	−0.431940	+	0.901902i	$0.642171\pi$
$3$	−0.442289	+	0.896873i	−0.255355	+	0.517810i
$3$	−0.442289	+	0.896873i	−0.255355	+	0.517810i
$4$	−1.18674	−	0.317986i	−0.593371	−	0.158993i
$5$	3.24146	+	2.84269i	1.44963	+	1.27129i	0.900009	+	0.435871i	$0.143560\pi$
$5$	3.24146	+	2.84269i	1.44963	+	1.27129i	0.549617	+	0.835417i	$0.314774\pi$
$6$	0.487952	−	0.730272i	0.199206	−	0.298132i
$7$	−2.13834	+	1.55805i	−0.808216	+	0.588886i
$7$	−2.13834	+	1.55805i	−0.808216	+	0.588886i
$8$	2.61980	+	1.08516i	0.926240	+	0.383661i
$9$	−0.608761	−	0.793353i	−0.202920	−	0.264451i
$10$	−2.49670	−	2.84695i	−0.789527	−	0.900283i
$11$	−2.31301	−	0.151603i	−0.697399	−	0.0457099i	−0.287420	−	0.957805i	$-0.592797\pi$
$11$	−2.31301	−	0.151603i	−0.697399	−	0.0457099i	−0.409979	+	0.912095i	$0.634464\pi$
$12$	0.810076	−	0.923714i	0.233849	−	0.266653i
$13$	1.06136	−	1.06136i	0.294369	−	0.294369i	−0.544434	−	0.838803i	$-0.683256\pi$
$13$	1.06136	−	1.06136i	0.294369	−	0.294369i	0.838803	+	0.544434i	$0.183256\pi$
$14$	2.04063	−	1.11157i	0.545381	−	0.297080i
$15$	−3.98319	+	1.64989i	−1.02846	+	0.426000i
$16$	−0.0288541	−	0.0166589i	−0.00721352	−	0.00416473i
$17$	−3.25106	−	2.53587i	−0.788498	−	0.615038i
$17$	−3.25106	−	2.53587i	−0.788498	−	0.615038i
$18$	0.439145	+	0.760622i	0.103508	+	0.179280i
$19$	−0.579980	+	4.40539i	−0.133057	+	1.01067i	0.786467	+	0.617632i	$0.211908\pi$
$19$	−0.579980	+	4.40539i	−0.133057	+	1.01067i	−0.919524	+	0.393034i	$0.871426\pi$
$20$	−2.94284	−	4.40428i	−0.658040	−	0.984826i
$21$	−0.451605	−	2.60692i	−0.0985484	−	0.568877i
$22$	1.99674	+	0.397175i	0.425706	+	0.0846781i
$23$	−1.83737	+	0.906089i	−0.383118	+	0.188933i	−0.623641	−	0.781711i	$-0.714347\pi$
$23$	−1.83737	+	0.906089i	−0.383118	+	0.188933i	0.240524	+	0.970643i	$0.422681\pi$
$24$	−2.13196	+	1.86968i	−0.435184	+	0.381646i
$25$	1.77358	+	13.4717i	0.354716	+	2.69434i
$26$	−1.04588	+	0.802535i	−0.205115	+	0.157390i
$27$	0.980785	−	0.195090i	0.188752	−	0.0375451i
$28$	3.03309	−	1.16903i	0.573201	−	0.220927i
$29$	−0.649389	+	3.26470i	−0.120589	+	0.606240i	0.872475	+	0.488659i	$0.162514\pi$
$29$	−0.649389	+	3.26470i	−0.120589	+	0.606240i	−0.993063	+	0.117581i	$0.962486\pi$
$30$	3.65761	−	0.980054i	0.667786	−	0.178933i
$31$	−5.19406	−	2.56143i	−0.932881	−	0.460046i	−0.0886727	−	0.996061i	$-0.528263\pi$
$31$	−5.19406	−	2.56143i	−0.932881	−	0.460046i	−0.844209	+	0.536015i	$0.819929\pi$
$32$	−4.47614	−	3.43466i	−0.791276	−	0.607168i
$33$	1.15899	−	2.00742i	0.201754	−	0.349448i
$34$	2.54024	+	2.58087i	0.435647	+	0.442616i
$35$	−11.3604	−	1.02828i	−1.92025	−	0.173811i
$36$	0.470167	+	1.13508i	0.0783612	+	0.189181i
$37$	0.361233	+	5.51135i	0.0593863	+	0.906060i	0.918786	+	0.394756i	$0.129171\pi$
$37$	0.361233	+	5.51135i	0.0593863	+	0.906060i	−0.859400	+	0.511304i	$0.829163\pi$
$38$	1.01007	−	3.76962i	0.163854	−	0.611513i
$39$	0.482478	+	1.42134i	0.0772584	+	0.227596i
$40$	5.40723	+	10.9648i	0.854958	+	1.73368i
$41$	0.575032	+	2.89088i	0.0898049	+	0.451480i	0.999356	+	0.0358873i	$0.0114257\pi$
$41$	0.575032	+	2.89088i	0.0898049	+	0.451480i	−0.909551	+	0.415592i	$0.863574\pi$
$42$	0.0943899	+	2.32182i	0.0145647	+	0.358265i
$43$	−3.01755	+	7.28500i	−0.460172	+	1.11095i	0.508155	+	0.861266i	$0.330328\pi$
$43$	−3.01755	+	7.28500i	−0.460172	+	1.11095i	−0.968327	+	0.249687i	$0.919672\pi$
$44$	2.69674	+	0.915419i	0.406549	+	0.138005i
$45$	0.281977	−	4.30214i	0.0420347	−	0.641325i
$46$	1.70381	−	0.578366i	0.251213	−	0.0852754i
$47$	−0.997470	−	3.72261i	−0.145496	−	0.542998i	−0.999733	−	0.0231143i	$-0.992642\pi$
$47$	−0.997470	−	3.72261i	−0.145496	−	0.542998i	0.854237	−	0.519884i	$-0.174025\pi$
$48$	0.0277028	−	0.0185104i	0.00399855	−	0.00267175i
$49$	2.14499	−	6.66326i	0.306427	−	0.951894i
$50$		−	11.9342i		−	1.68775i
$51$	3.71226	−	1.79420i	0.519820	−	0.251238i
$52$	−1.59706	+	0.922064i	−0.221473	+	0.127867i
$53$	6.82093	−	8.88921i	0.936926	−	1.22103i	−0.0381760	−	0.999271i	$-0.512155\pi$
$53$	6.82093	−	8.88921i	0.936926	−	1.22103i	0.975102	−	0.221755i	$-0.0711786\pi$
$54$	−0.876410	+	0.0574430i	−0.119264	+	0.00781700i
$55$	−7.06658	−	7.06658i	−0.952857	−	0.952857i
$56$	−7.29275	+	1.76134i	−0.974535	+	0.235369i
$57$	−3.69455	−	2.46862i	−0.489356	−	0.326977i
$58$	0.939738	−	2.76838i	0.123394	−	0.363506i
$59$	7.24418	−	0.953715i	0.943112	−	0.124163i	0.356739	−	0.934204i	$-0.383889\pi$
$59$	7.24418	−	0.953715i	0.943112	−	0.124163i	0.586373	+	0.810041i	$0.300555\pi$
$60$	5.25166	−	0.691394i	0.677986	−	0.0892586i
$61$	−0.451353	+	1.32964i	−0.0577898	+	0.170243i	−0.971991	−	0.235016i	$-0.924486\pi$
$61$	−0.451353	+	1.32964i	−0.0577898	+	0.170243i	0.914202	+	0.405260i	$0.132819\pi$
$62$	4.22923	+	2.82588i	0.537113	+	0.358887i
$63$	2.53782	+	0.747980i	0.319735	+	0.0942367i
$64$	3.55108	+	3.55108i	0.443886	+	0.443886i
$65$	6.45749	−	0.423246i	0.800953	−	0.0524972i
$66$	−1.23935	+	1.61515i	−0.152553	+	0.198811i
$67$	11.8097	−	6.81835i	1.44279	−	0.832994i	0.444752	−	0.895654i	$-0.353292\pi$
$67$	11.8097	−	6.81835i	1.44279	−	0.832994i	0.998035	+	0.0626600i	$0.0199584\pi$
$68$	3.05180	+	4.04321i	0.370085	+	0.490311i
$69$		−	2.04864i		−	0.246627i
$70$	9.77447	+	2.19776i	1.16827	+	0.262682i
$71$	−10.2549	+	6.85214i	−1.21704	+	0.813199i	−0.987115	−	0.160010i	$-0.948847\pi$
$71$	−10.2549	+	6.85214i	−1.21704	+	0.813199i	−0.229923	+	0.973209i	$0.573847\pi$
$72$	−0.733921	−	2.73903i	−0.0864935	−	0.322798i
$73$	2.27983	−	0.773899i	0.266834	−	0.0905780i	−0.184816	−	0.982773i	$-0.559169\pi$
$73$	2.27983	−	0.773899i	0.266834	−	0.0905780i	0.451650	+	0.892195i	$0.350836\pi$
$74$	0.317267	−	4.84056i	0.0368816	−	0.562704i
$75$	−12.8668	−	4.36770i	−1.48573	−	0.504339i
$76$	2.08914	−	5.04363i	0.239641	−	0.578544i
$77$	5.18220	−	3.27960i	0.590567	−	0.373745i
$78$	−0.257189	−	1.29298i	−0.0291209	−	0.146401i
$79$	6.20687	+	12.5863i	0.698328	+	1.41607i	0.899680	+	0.436550i	$0.143800\pi$
$79$	6.20687	+	12.5863i	0.698328	+	1.41607i	−0.201353	+	0.979519i	$0.564534\pi$
$80$	−0.0461734	−	0.136022i	−0.00516234	−	0.0152078i
$81$	−0.258819	+	0.965926i	−0.0287577	+	0.107325i
$82$	−0.169314	−	2.58323i	−0.0186976	−	0.285270i
$83$	0.458903	+	1.10789i	0.0503712	+	0.121607i	0.947062	−	0.321050i	$-0.104036\pi$
$83$	0.458903	+	1.10789i	0.0503712	+	0.121607i	−0.896691	+	0.442657i	$0.854036\pi$
$84$	−0.293028	+	3.23735i	−0.0319719	+	0.353224i
$85$	−3.32951	−	17.4617i	−0.361137	−	1.89398i
$86$	3.46276	−	5.99768i	0.373399	−	0.646746i
$87$	−2.64080	−	2.02636i	−0.283124	−	0.217249i
$88$	−5.89512	−	2.90715i	−0.628422	−	0.309903i
$89$	5.85285	−	1.56827i	0.620401	−	0.166236i	0.0650908	−	0.997879i	$-0.479266\pi$
$89$	5.85285	−	1.56827i	0.620401	−	0.166236i	0.555310	+	0.831643i	$0.312600\pi$
$90$	−0.738737	+	3.71388i	−0.0778697	+	0.391477i
$91$	−0.615902	+	3.92320i	−0.0645641	+	0.411264i
$92$	2.46860	−	0.491036i	0.257370	−	0.0511940i
$93$	4.59455	−	3.52552i	0.476433	−	0.365580i
$94$	0.441814	+	3.35591i	0.0455696	+	0.346136i
$95$	−14.4031	+	12.6312i	−1.47773	+	1.29593i
$96$	5.06020	−	2.49541i	0.516454	−	0.254687i
$97$	−3.69653	−	0.735286i	−0.375326	−	0.0746570i	0.00382284	−	0.999993i	$-0.498783\pi$
$97$	−3.69653	−	0.735286i	−0.375326	−	0.0746570i	−0.379149	+	0.925336i	$0.623783\pi$
$98$	−2.63168	+	5.55631i	−0.265840	+	0.561272i
$99$	1.28780	+	1.92732i	0.129428	+	0.193703i
$100$	2.17903	−	16.5514i	0.217903	−	1.65514i
$101$	5.80300	+	10.0511i	0.577420	+	1.00012i	0.995774	+	0.0918367i	$0.0292738\pi$
$101$	5.80300	+	10.0511i	0.577420	+	1.00012i	−0.418354	+	0.908284i	$0.637393\pi$
$102$	−3.43823	+	1.13678i	−0.340436	+	0.112558i
$103$	0.665896	+	0.384455i	0.0656127	+	0.0378815i	0.532447	−	0.846463i	$-0.321272\pi$
$103$	0.665896	+	0.384455i	0.0656127	+	0.0378815i	−0.466835	+	0.884345i	$0.654606\pi$
$104$	3.93231	−	1.62881i	0.385594	−	0.159718i
$105$	5.94680	−	9.73402i	0.580349	−	0.949943i
$106$	−6.95856	+	6.95856i	−0.675875	+	0.675875i
$107$	8.48081	−	9.67051i	0.819871	−	0.934883i	−0.178929	−	0.983862i	$-0.557263\pi$
$107$	8.48081	−	9.67051i	0.819871	−	0.934883i	0.998800	+	0.0489787i	$0.0155966\pi$
$108$	−1.22597	−	0.0803546i	−0.117969	−	0.00773213i
$109$	4.15603	+	4.73905i	0.398076	+	0.453919i	0.915803	−	0.401627i	$-0.131555\pi$
$109$	4.15603	+	4.73905i	0.398076	+	0.453919i	−0.517727	+	0.855546i	$0.673222\pi$
$110$	5.34330	+	6.96352i	0.509463	+	0.663946i
$111$	−5.10275	−	2.11363i	−0.484331	−	0.200617i
$112$	0.0876552	−	0.00933358i	0.00828264	−	0.000881940i
$113$	7.00889	−	10.4895i	0.659341	−	0.986773i	−0.339591	−	0.940573i	$-0.610289\pi$
$113$	7.00889	−	10.4895i	0.659341	−	0.986773i	0.998932	−	0.0462004i	$-0.0147113\pi$
$114$	2.93413	+	2.57316i	0.274806	+	0.240999i
$115$	−8.53148	−	2.28600i	−0.795565	−	0.213171i
$116$	1.80879	−	3.66786i	0.167942	−	0.340552i
$117$	−1.48815	−	0.195919i	−0.137580	−	0.0181127i
$118$	−6.41740			−0.590770
$119$	10.9029	+	0.357243i	0.999464	+	0.0327484i
$120$	−12.2256			−1.11604
$121$	−5.57886	−	0.734471i	−0.507169	−	0.0667701i
$122$	0.545458	−	1.10608i	0.0493834	−	0.100140i
$123$	−2.84708	−	0.762874i	−0.256713	−	0.0687860i
$124$	5.34951	+	4.69140i	0.480400	+	0.421300i
$125$	−20.5704	+	30.7858i	−1.83988	+	2.75357i
$126$	−2.12413	−	0.942259i	−0.189232	−	0.0839431i
$127$	1.80484	+	0.747590i	0.160154	+	0.0663379i	0.461320	−	0.887234i	$-0.347376\pi$
$127$	1.80484	+	0.747590i	0.160154	+	0.0663379i	−0.301166	+	0.953572i	$0.597376\pi$
$128$	4.18421	+	5.45297i	0.369836	+	0.481979i
$129$	−5.19909	−	5.92843i	−0.457755	−	0.521969i
$130$	−5.67155	−	0.371733i	−0.497428	−	0.0326031i
$131$	4.57794	−	5.22014i	0.399976	−	0.456085i	−0.516433	−	0.856327i	$-0.672741\pi$
$131$	4.57794	−	5.22014i	0.399976	−	0.456085i	0.916409	+	0.400242i	$0.131074\pi$
$132$	−2.01375	+	2.01375i	−0.175275	+	0.175275i
$133$	−5.62360	−	10.3238i	−0.487628	−	0.895191i
$134$	−11.0653	+	4.58339i	−0.955895	+	0.395945i
$135$	3.73376	+	2.15569i	0.321351	+	0.185532i
$136$	−5.76532	−	10.1714i	−0.494372	−	0.872189i
$137$	−5.25450	−	9.10105i	−0.448922	−	0.777555i	0.549394	−	0.835563i	$-0.314859\pi$
$137$	−5.25450	−	9.10105i	−0.448922	−	0.777555i	−0.998316	+	0.0580078i	$0.981525\pi$
$138$	−0.234856	+	1.78391i	−0.0199922	+	0.151856i
$139$	9.26085	+	13.8598i	0.785495	+	1.17558i	0.980835	+	0.194841i	$0.0624191\pi$
$139$	9.26085	+	13.8598i	0.785495	+	1.17558i	−0.195340	+	0.980736i	$0.562581\pi$
$140$	13.1549	+	4.83275i	1.11179	+	0.408442i
$141$	3.77988	+	0.751864i	0.318323	+	0.0633184i
$142$	9.71530	−	4.79105i	0.815290	−	0.402056i
$143$	−2.61585	+	2.29404i	−0.218748	+	0.191837i
$144$	0.00434885	+	0.0330328i	0.000362404	+	0.00275273i
$145$	−11.3855	+	8.73639i	−0.945513	+	0.725518i
$146$	−2.07395	+	0.412533i	−0.171641	+	0.0341415i
$147$	5.02739	+	4.87087i	0.414652	+	0.401742i
$148$	1.32384	−	6.65541i	0.108819	−	0.547072i
$149$	16.6329	−	4.45678i	1.36262	−	0.365113i	0.497843	−	0.867267i	$-0.334125\pi$
$149$	16.6329	−	4.45678i	1.36262	−	0.365113i	0.864778	+	0.502154i	$0.167459\pi$
$150$	10.7034	+	5.27834i	0.873931	+	0.430975i
$151$	10.8715	+	8.34202i	0.884713	+	0.678864i	0.947704	−	0.319150i	$-0.103397\pi$
$151$	10.8715	+	8.34202i	0.884713	+	0.678864i	−0.0629911	+	0.998014i	$0.520064\pi$
$152$	−6.29998	+	10.9119i	−0.510996	+	0.885070i
$153$	−0.0327183	+	4.12298i	−0.00264512	+	0.333323i
$154$	−4.88852	+	2.26171i	−0.393928	+	0.182254i
$155$	−9.55502	−	23.0679i	−0.767478	−	1.85286i
$156$	−0.120612	−	1.84018i	−0.00965667	−	0.147332i
$157$	−3.55601	+	13.2712i	−0.283801	+	1.05916i	0.665911	+	0.746031i	$0.268043\pi$
$157$	−3.55601	+	13.2712i	−0.283801	+	1.05916i	−0.949711	+	0.313127i	$0.898624\pi$
$158$	−3.96191	−	11.6714i	−0.315193	−	0.928527i
$159$	4.95567	+	10.0491i	0.393010	+	0.796945i
$160$	−4.74557	−	23.8576i	−0.375170	−	1.88611i
$161$	2.51719	−	4.80023i	0.198382	−	0.378311i
$162$	0.336107	−	0.811435i	0.0264071	−	0.0637523i
$163$	−11.2649	−	3.82392i	−0.882336	−	0.299513i	−0.156745	−	0.987639i	$-0.550100\pi$
$163$	−11.2649	−	3.82392i	−0.882336	−	0.299513i	−0.725591	+	0.688127i	$0.758433\pi$
$164$	0.236847	−	3.61358i	0.0184946	−	0.282173i
$165$	9.46329	−	3.21235i	0.736716	−	0.250081i
$166$	−0.272594	−	1.01733i	−0.0211574	−	0.0789604i
$167$	−13.8711	+	9.26837i	−1.07338	+	0.717208i	−0.961025	−	0.276461i	$-0.910838\pi$
$167$	−13.8711	+	9.26837i	−1.07338	+	0.717208i	−0.112352	+	0.993668i	$0.535838\pi$
$168$	1.64581	−	7.31969i	0.126977	−	0.564726i
$169$			10.7470i			0.826694i
$170$	0.897461	+	15.5869i	0.0688321	+	1.19546i
$171$	3.84810	−	2.22170i	0.294271	−	0.169898i
$172$	5.89758	−	7.68588i	0.449686	−	0.586043i
$173$	8.63768	−	0.566143i	0.656710	−	0.0430431i	0.266594	−	0.963809i	$-0.414102\pi$
$173$	8.63768	−	0.566143i	0.656710	−	0.0430431i	0.390116	+	0.920766i	$0.372435\pi$
$174$	2.06725	+	2.06725i	0.156718	+	0.156718i
$175$	−24.7820	−	26.0437i	−1.87335	−	1.96872i
$176$	0.0642143	+	0.0429066i	0.00484033	+	0.00323421i
$177$	−2.34866	+	6.91893i	−0.176536	+	0.520058i
$178$	−5.27631	+	0.694640i	−0.395476	+	0.0520654i
$179$	−0.461412	+	0.0607461i	−0.0344876	+	0.00454037i	−0.147750	−	0.989025i	$-0.547203\pi$
$179$	−0.461412	+	0.0607461i	−0.0344876	+	0.00454037i	0.113263	+	0.993565i	$0.463870\pi$
$180$	−1.70266	+	5.01587i	−0.126909	+	0.373861i
$181$	0.0908091	+	0.0606767i	0.00674979	+	0.00451006i	0.558941	−	0.829208i	$-0.311208\pi$
$181$	0.0908091	+	0.0606767i	0.00674979	+	0.00451006i	−0.552191	+	0.833718i	$0.686208\pi$
$182$	0.986069	−	3.34563i	0.0730923	−	0.247994i
$183$	−0.992892	−	0.992892i	−0.0733967	−	0.0733967i
$184$	−5.79679	+	0.379942i	−0.427345	+	0.0280097i
$185$	−14.4961	+	18.8917i	−1.06577	+	1.38894i
$186$	−4.40499	+	2.54322i	−0.322990	+	0.186478i
$187$	7.13529	+	6.35835i	0.521784	+	0.464969i
$188$			4.73496i			0.345332i
$189$	−1.79329	+	1.94528i	−0.130443	+	0.141498i
$190$	13.9899	−	9.34778i	1.01494	−	0.678159i
$191$	−5.16709	−	19.2838i	−0.373878	−	1.39533i	−0.854978	−	0.518664i	$-0.826429\pi$
$191$	−5.16709	−	19.2838i	−0.373878	−	1.39533i	0.481100	−	0.876666i	$-0.340237\pi$
$192$	−4.75548	+	1.61427i	−0.343197	+	0.116500i
$193$	−1.62400	+	24.7774i	−0.116898	+	1.78352i	0.389312	+	0.921106i	$0.372713\pi$
$193$	−1.62400	+	24.7774i	−0.116898	+	1.78352i	−0.506210	+	0.862410i	$0.668954\pi$
$194$	3.13456	+	1.06404i	0.225048	+	0.0763936i
$195$	−2.47648	+	5.97874i	−0.177344	+	0.428147i
$196$	−4.66437	+	7.22549i	−0.333170	+	0.516106i
$197$	5.27479	+	26.5182i	0.375813	+	1.88934i	0.451606	+	0.892218i	$0.350851\pi$
$197$	5.27479	+	26.5182i	0.375813	+	1.88934i	−0.0757926	+	0.997124i	$0.524149\pi$
$198$	−0.900435	−	1.82590i	−0.0639911	−	0.129761i
$199$	0.524776	+	1.54594i	0.0372004	+	0.109589i	0.963944	−	0.266106i	$-0.0857373\pi$
$199$	0.524776	+	1.54594i	0.0372004	+	0.109589i	−0.926743	+	0.375695i	$0.877404\pi$
$200$	−9.97248	+	37.2178i	−0.705161	+	2.63170i
$201$	0.891882	+	13.6075i	0.0629085	+	0.959799i
$202$	−3.90086	−	9.41751i	−0.274464	−	0.662614i
$203$	−3.69794	−	7.99281i	−0.259544	−	0.560986i
$204$	−4.97602	+	0.948807i	−0.348391	+	0.0664297i
$205$	−6.35392	+	11.0053i	−0.443777	+	0.768645i
$206$	−0.535773	−	0.411113i	−0.0373291	−	0.0286436i
$207$	1.83737	+	0.906089i	0.127706	+	0.0629776i
$208$	−0.0483058	+	0.0129435i	−0.00334941	+	0.000897471i
$209$	2.00937	−	10.1018i	0.138991	−	0.698755i
$210$	−6.29425	+	7.79442i	−0.434344	+	0.537866i
$211$	16.4292	−	3.26798i	1.13103	−	0.224977i	0.406123	−	0.913818i	$-0.366881\pi$
$211$	16.4292	−	3.26798i	1.13103	−	0.224977i	0.724912	+	0.688842i	$0.241881\pi$
$212$	−10.9213	+	8.38023i	−0.750080	+	0.575556i
$213$	−1.60985	−	12.2280i	−0.110305	−	0.837849i
$214$	−8.49352	+	7.44861i	−0.580605	+	0.509177i
$215$	−30.4902	+	15.0361i	−2.07942	+	1.02545i
$216$	2.78117	+	0.553209i	0.189235	+	0.0376411i
$217$	15.0975	−	2.61538i	1.02488	−	0.177544i
$218$	−3.07569	−	4.60310i	−0.208312	−	0.311761i
$219$	−0.314255	+	2.38701i	−0.0212354	+	0.161299i
$220$	6.13912	+	10.6333i	0.413900	+	0.716895i
$221$	−6.14203	+	0.759079i	−0.413157	+	0.0510612i
$222$	4.20105	+	2.42548i	0.281956	+	0.162787i
$223$	5.43069	−	2.24947i	0.363666	−	0.150635i	−0.193365	−	0.981127i	$-0.561940\pi$
$223$	5.43069	−	2.24947i	0.363666	−	0.150635i	0.557031	+	0.830491i	$0.311940\pi$
$224$	14.9229	+	0.370444i	0.997075	+	0.0247513i
$225$	9.60812	−	9.60812i	0.640542	−	0.640542i
$226$	−7.30570	+	8.33055i	−0.485968	+	0.554140i
$227$	−15.0626	−	0.987257i	−0.999742	−	0.0655266i	−0.443266	−	0.896390i	$-0.646180\pi$
$227$	−15.0626	−	0.987257i	−0.999742	−	0.0655266i	−0.556476	+	0.830864i	$0.687847\pi$
$228$	3.59949	+	4.10443i	0.238382	+	0.271823i
$229$	−4.13021	−	5.38260i	−0.272932	−	0.355692i	0.636697	−	0.771114i	$-0.280300\pi$
$229$	−4.13021	−	5.38260i	−0.272932	−	0.355692i	−0.909629	+	0.415423i	$0.863634\pi$
$230$	7.16695	+	2.96865i	0.472575	+	0.195747i
$231$	0.649351	+	6.09831i	0.0427242	+	0.401239i
$232$	−5.24399	+	7.84818i	−0.344285	+	0.515258i
$233$	−5.07566	−	4.45124i	−0.332518	−	0.291610i	0.476764	−	0.879032i	$-0.341810\pi$
$233$	−5.07566	−	4.45124i	−0.332518	−	0.291610i	−0.809281	+	0.587421i	$0.800143\pi$
$234$	1.27339	+	0.341203i	0.0832440	+	0.0223052i
$235$	7.34895	−	14.9022i	0.479392	−	0.972112i
$236$	−8.90024	−	1.17174i	−0.579356	−	0.0762737i
$237$	−14.0335			−0.911576
$238$	−9.45300	−	1.56098i	−0.612747	−	0.101183i
$239$	21.3991			1.38419			0.692095	−	0.721806i	$-0.256688\pi$
$239$	21.3991			1.38419			0.692095	+	0.721806i	$0.256688\pi$
$240$	0.142417	+	0.0187495i	0.00919296	+	0.00121028i
$241$	2.63017	−	5.33347i	0.169424	−	0.343559i	−0.795556	−	0.605880i	$-0.792821\pi$
$241$	2.63017	−	5.33347i	0.169424	−	0.343559i	0.964981	+	0.262321i	$0.0844879\pi$
$242$	4.77374	+	1.27912i	0.306868	+	0.0822250i
$243$	−0.751840	−	0.659346i	−0.0482305	−	0.0422971i
$244$	0.958448	−	1.43442i	0.0613584	−	0.0918293i
$245$	25.8945	−	15.5012i	1.65434	−	0.990334i
$246$	2.39172	+	0.990682i	0.152490	+	0.0631636i
$247$	4.06014	+	5.29128i	0.258341	+	0.336676i
$248$	−10.8279	−	12.3468i	−0.687570	−	0.784024i
$249$	−1.19660	−	0.0784296i	−0.0758317	−	0.00497027i
$250$	21.4415	−	24.4494i	1.35608	−	1.54632i
$251$	7.68043	−	7.68043i	0.484785	−	0.484785i	−0.421871	−	0.906656i	$-0.638627\pi$
$251$	7.68043	−	7.68043i	0.484785	−	0.484785i	0.906656	+	0.421871i	$0.138627\pi$
$252$	−2.77389	−	1.69465i	−0.174739	−	0.106753i
$253$	4.38721	−	1.81724i	0.275822	−	0.114249i
$254$	−1.48591	−	0.857891i	−0.0932343	−	0.0538288i
$255$	17.1335	+	4.73694i	1.07294	+	0.296639i
$256$	−8.04038	−	13.9263i	−0.502524	−	0.870397i
$257$	3.44618	−	26.1763i	0.214967	−	1.63283i	−0.455035	−	0.890474i	$-0.650373\pi$
$257$	3.44618	−	26.1763i	0.214967	−	1.63283i	0.670001	−	0.742360i	$-0.266294\pi$
$258$	3.84762	+	5.75836i	0.239542	+	0.358500i
$259$	−9.35937	−	11.2223i	−0.581563	−	0.697320i
$260$	−7.79796	−	1.55111i	−0.483609	−	0.0961957i
$261$	2.98538	−	1.47223i	0.184791	−	0.0911287i
$262$	−4.58480	+	4.02076i	−0.283250	+	0.248403i
$263$	1.06181	+	8.06523i	0.0654739	+	0.497323i	0.992492	+	0.122307i	$0.0390294\pi$
$263$	1.06181	+	8.06523i	0.0654739	+	0.497323i	−0.927018	+	0.375016i	$0.877637\pi$
$264$	5.21469	−	4.00137i	0.320942	−	0.246267i
$265$	47.3790	−	9.42427i	2.91047	−	0.578928i
$266$	3.71338	+	9.63446i	0.227682	+	0.590727i
$267$	−1.18211	+	5.94289i	−0.0723442	+	0.363699i
$268$	−16.1832	+	4.33628i	−0.988548	+	0.264881i
$269$	18.2107	+	8.98051i	1.11032	+	0.547552i	0.902533	−	0.430622i	$-0.141706\pi$
$269$	18.2107	+	8.98051i	1.11032	+	0.547552i	0.207792	+	0.978173i	$0.433372\pi$
$270$	−3.00414	−	2.30516i	−0.182826	−	0.140288i
$271$	−6.00589	+	10.4025i	−0.364832	+	0.631908i	−0.988749	−	0.149583i	$-0.952207\pi$
$271$	−6.00589	+	10.4025i	−0.364832	+	0.631908i	0.623917	+	0.781490i	$0.285540\pi$
$272$	0.0515616	+	0.127329i	0.00312638	+	0.00772047i
$273$	−3.24621	−	2.28757i	−0.196469	−	0.138450i
$274$	3.53215	+	8.52736i	0.213385	+	0.515157i
$275$	−2.05997	−	31.4290i	−0.124221	−	1.89524i
$276$	−0.651439	+	2.43120i	−0.0392120	+	0.146341i
$277$	−9.99981	−	29.4585i	−0.600830	−	1.76999i	−0.637255	−	0.770653i	$-0.719930\pi$
$277$	−9.99981	−	29.4585i	−0.600830	−	1.76999i	0.0364251	−	0.999336i	$-0.488403\pi$
$278$	−6.47524	−	13.1305i	−0.388359	−	0.787515i
$279$	1.12983	+	5.68003i	0.0676410	+	0.340054i
$280$	−28.6461	−	15.0217i	−1.71193	−	0.897718i
$281$	0.657744	−	1.58794i	0.0392377	−	0.0947283i	−0.903046	−	0.429544i	$-0.858674\pi$
$281$	0.657744	−	1.58794i	0.0392377	−	0.0947283i	0.942284	+	0.334816i	$0.108674\pi$
$282$	−3.20523	−	1.08803i	−0.190869	−	0.0647913i
$283$	1.59709	−	24.3669i	0.0949374	−	1.44846i	−0.638979	−	0.769224i	$-0.720643\pi$
$283$	1.59709	−	24.3669i	0.0949374	−	1.44846i	0.733916	−	0.679240i	$-0.237690\pi$
$284$	14.3489	−	4.87078i	0.851448	−	0.289028i
$285$	−4.95824	−	18.5044i	−0.293701	−	1.09611i
$286$	2.54081	−	1.69771i	0.150241	−	0.100388i
$287$	−5.73374	−	5.28576i	−0.338452	−	0.312008i
$288$			5.64205i			0.332461i
$289$	4.13877	+	16.4885i	0.243457	+	0.969912i
$290$	10.9158	−	6.30222i	0.640995	−	0.370079i
$291$	2.29439	−	2.99011i	0.134500	−	0.175283i
$292$	−2.95166	+	0.193462i	−0.172733	+	0.0113215i
$293$	−20.2743	−	20.2743i	−1.18443	−	1.18443i	−0.978583	−	0.205851i	$-0.934004\pi$
$293$	−20.2743	−	20.2743i	−1.18443	−	1.18443i	−0.205851	−	0.978583i	$-0.565996\pi$
$294$	−3.81934	−	4.81778i	−0.222748	−	0.280978i
$295$	26.1929	+	17.5015i	1.52501	+	1.01898i
$296$	−5.03432	+	14.8306i	−0.292614	+	0.862013i
$297$	−2.29814	+	0.302556i	−0.133352	+	0.0175561i
$298$	−14.9945	+	1.97406i	−0.868607	+	0.114354i
$299$	−0.988424	+	2.91180i	−0.0571620	+	0.168394i
$300$	13.8807	+	9.27481i	0.801404	+	0.535481i
$301$	−4.89783	−	20.2793i	−0.282306	−	1.16888i
$302$	−8.51035	−	8.51035i	−0.489716	−	0.489716i
$303$	−11.5811	+	0.759069i	−0.665320	+	0.0436074i
$304$	0.0901238	−	0.117452i	0.00516896	−	0.00673631i
$305$	−5.24280	+	3.02693i	−0.300202	+	0.173322i
$306$	0.501148	−	3.58644i	0.0286487	−	0.205023i
$307$		−	5.84751i		−	0.333735i	−0.985979	−	0.166867i	$-0.946635\pi$
$307$		−	5.84751i		−	0.333735i	0.985979	−	0.166867i	$-0.0533652\pi$
$308$	−7.19280	+	2.24416i	−0.409848	+	0.127873i
$309$	−0.639326	+	0.427184i	−0.0363700	+	0.0243016i
$310$	5.67579	+	21.1824i	0.322363	+	1.20308i
$311$	3.27971	−	1.11331i	0.185975	−	0.0631302i	−0.226898	−	0.973918i	$-0.572858\pi$
$311$	3.27971	−	1.11331i	0.185975	−	0.0631302i	0.412874	+	0.910788i	$0.364525\pi$
$312$	−0.278375	+	4.24718i	−0.0157599	+	0.240449i
$313$	2.24385	+	0.761683i	0.126830	+	0.0430529i	0.384133	−	0.923278i	$-0.374501\pi$
$313$	2.24385	+	0.761683i	0.126830	+	0.0430529i	−0.257303	+	0.966331i	$0.582834\pi$
$314$	4.61790	−	11.1486i	0.260603	−	0.629152i
$315$	6.09997	+	9.63877i	0.343694	+	0.543083i
$316$	−3.36368	−	16.9104i	−0.189222	−	0.951283i
$317$	2.19142	+	4.44376i	0.123083	+	0.249587i	0.949690	−	0.313193i	$-0.101399\pi$
$317$	2.19142	+	4.44376i	0.123083	+	0.249587i	−0.826607	+	0.562780i	$0.809732\pi$
$318$	−3.16325	−	9.31864i	−0.177386	−	0.522563i
$319$	1.99698	−	7.45284i	0.111809	−	0.417279i
$320$	1.41609	+	21.6053i	0.0791617	+	1.20777i
$321$	4.92225	+	11.8834i	0.274733	+	0.663265i
$322$	−2.74220	+	3.89136i	−0.152817	+	0.216857i
$323$	13.0570	−	12.8514i	0.726512	−	0.715072i
$324$	0.614303	−	1.06400i	0.0341279	−	0.0591113i
$325$	16.1808	+	12.4159i	0.897547	+	0.688712i
$326$	9.37085	+	4.62119i	0.519003	+	0.255944i
$327$	−6.08849	+	1.63141i	−0.336694	+	0.0902170i
$328$	−1.63059	+	8.19754i	−0.0900344	+	0.452633i
$329$	7.93292	+	6.40610i	0.437356	+	0.353179i
$330$	−8.60867	+	1.71237i	−0.473892	+	0.0942630i
$331$	−7.95505	+	6.10413i	−0.437249	+	0.335513i	−0.803815	−	0.594879i	$-0.797200\pi$
$331$	−7.95505	+	6.10413i	−0.437249	+	0.335513i	0.366566	+	0.930392i	$0.380533\pi$
$332$	−0.192305	−	1.46070i	−0.0105541	−	0.0801666i
$333$	4.15254	−	3.64168i	0.227558	−	0.199563i
$334$	13.1412	−	6.48050i	0.719052	−	0.354597i
$335$	57.6632	+	11.4699i	3.15048	+	0.626669i
$336$	−0.0303979	+	0.0827437i	−0.00165834	+	0.00451404i
$337$	4.89520	+	7.32618i	0.266658	+	0.399083i	0.940500	−	0.339793i	$-0.110357\pi$
$337$	4.89520	+	7.32618i	0.266658	+	0.399083i	−0.673842	+	0.738876i	$0.735357\pi$
$338$	1.23204	−	9.35825i	0.0670140	−	0.509022i
$339$	6.30783	+	10.9255i	0.342595	+	0.593391i
$340$	−1.60130	+	21.7812i	−0.0868425	+	1.18125i
$341$	11.6256	+	6.71204i	0.629562	+	0.363478i
$342$	−3.60553	+	1.49346i	−0.194965	+	0.0807571i
$343$	5.79495	+	17.5903i	0.312898	+	0.949787i
$344$	−15.8108	+	15.8108i	−0.852459	+	0.852459i
$345$	5.82363	−	6.64058i	0.313534	−	0.357517i
$346$	−7.58639	−	0.497238i	−0.407847	−	0.0267317i
$347$	2.49312	+	2.84286i	0.133838	+	0.152613i	0.814876	−	0.579635i	$-0.196805\pi$
$347$	2.49312	+	2.84286i	0.133838	+	0.152613i	−0.681039	+	0.732248i	$0.738471\pi$
$348$	2.48960	+	3.24451i	0.133456	+	0.173924i
$349$	−28.5209	−	11.8137i	−1.52669	−	0.632375i	−0.547770	−	0.836629i	$-0.684523\pi$
$349$	−28.5209	−	11.8137i	−1.52669	−	0.632375i	−0.978918	+	0.204254i	$0.934523\pi$
$350$	18.5940	+	25.5193i	0.993889	+	1.36406i
$351$	0.833907	−	1.24803i	0.0445107	−	0.0666149i
$352$	9.83264	+	8.62300i	0.524082	+	0.459607i
$353$	−11.8989	−	3.18829i	−0.633313	−	0.169696i	−0.0721401	−	0.997395i	$-0.522983\pi$
$353$	−11.8989	−	3.18829i	−0.633313	−	0.169696i	−0.561172	+	0.827699i	$0.689650\pi$
$354$	2.83834	−	5.75559i	0.150856	−	0.305906i
$355$	−52.7195	−	6.94065i	−2.79806	−	0.368372i
$356$	−7.44451			−0.394558
$357$	−5.14261	+	9.62047i	−0.272176	+	0.509169i
$358$	0.408751			0.0216032
$359$	−2.88498	−	0.379815i	−0.152263	−	0.0200458i	0.0540092	−	0.998540i	$-0.482800\pi$
$359$	−2.88498	−	0.379815i	−0.152263	−	0.0200458i	−0.206272	+	0.978495i	$0.566133\pi$
$360$	5.40723	−	10.9648i	0.284986	−	0.577894i
$361$	−0.718478	−	0.192515i	−0.0378146	−	0.0101324i
$362$	−0.0721185	−	0.0632462i	−0.00379046	−	0.00332415i
$363$	3.12619	−	4.67868i	0.164083	−	0.245567i
$364$	1.97844	−	4.45998i	0.103699	−	0.233767i
$365$	9.58994	+	3.97228i	0.501961	+	0.207919i
$366$	0.750763	+	0.978413i	0.0392430	+	0.0511425i
$367$	−16.5041	−	18.8193i	−0.861507	−	0.982360i	0.138461	−	0.990368i	$-0.455784\pi$
$367$	−16.5041	−	18.8193i	−0.861507	−	0.982360i	−0.999968	+	0.00800769i	$0.997451\pi$
$368$	0.0681100	+	0.00446417i	0.00355048	+	0.000232711i
$369$	1.94343	−	2.21606i	0.101171	−	0.115364i
$370$	14.7886	−	14.7886i	0.768823	−	0.768823i
$371$	−0.735668	+	29.6354i	−0.0381940	+	1.53860i
$372$	−6.57361	+	2.72288i	−0.340826	+	0.141175i
$373$	15.3668	+	8.87204i	0.795664	+	0.459377i	0.841953	−	0.539551i	$-0.181406\pi$
$373$	15.3668	+	8.87204i	0.795664	+	0.459377i	−0.0462890	+	0.998928i	$0.514740\pi$
$374$	−5.48432	−	6.35469i	−0.283588	−	0.328593i
$375$	−18.5129	−	32.0653i	−0.956002	−	1.65584i
$376$	1.42644	−	10.8349i	0.0735632	−	0.558768i
$377$	2.77579	+	4.15427i	0.142961	+	0.213956i
$378$	1.78456	−	1.48832i	0.0917880	−	0.0765509i
$379$	8.15098	+	1.62133i	0.418688	+	0.0832822i	0.399938	−	0.916542i	$-0.369032\pi$
$379$	8.15098	+	1.62133i	0.418688	+	0.0832822i	0.0187495	+	0.999824i	$0.494032\pi$
$380$	21.1093	−	10.4100i	1.08289	−	0.534020i
$381$	−1.46875	+	1.28806i	−0.0752465	+	0.0659894i
$382$	2.28868	+	17.3843i	0.117099	+	0.889457i
$383$	−6.68912	+	5.13274i	−0.341798	+	0.262271i	−0.765369	−	0.643592i	$-0.777443\pi$
$383$	−6.68912	+	5.13274i	−0.341798	+	0.262271i	0.423570	+	0.905863i	$0.360777\pi$
$384$	−6.74125	+	1.34092i	−0.344013	+	0.0684285i
$385$	26.1208	+	4.10069i	1.33124	+	0.208990i
$386$	4.25462	−	21.3894i	0.216554	−	1.08869i
$387$	7.61655	−	2.04085i	0.387171	−	0.103742i
$388$	4.15302	+	2.04804i	0.210838	+	0.103974i
$389$	2.09323	+	1.60620i	0.106131	+	0.0814373i	0.660464	−	0.750858i	$-0.270360\pi$
$389$	2.09323	+	1.60620i	0.106131	+	0.0814373i	−0.554333	+	0.832295i	$0.687026\pi$
$390$	2.84186	−	4.92225i	0.143903	−	0.249248i
$391$	8.27111	+	1.71357i	0.418288	+	0.0866588i
$392$	12.8501	−	15.1288i	0.649030	−	0.764119i
$393$	2.65703	+	6.41463i	0.134029	+	0.323575i
$394$	−1.55312	−	23.6961i	−0.0782453	−	1.19379i
$395$	−15.6595	+	58.4422i	−0.787917	+	2.94054i
$396$	−0.915419	−	2.69674i	−0.0460015	−	0.135516i
$397$	−7.08908	−	14.3752i	−0.355791	−	0.721472i	0.643232	−	0.765671i	$-0.277593\pi$
$397$	−7.08908	−	14.3752i	−0.355791	−	0.721472i	−0.999023	+	0.0441993i	$0.985926\pi$
$398$	−0.279736	−	1.40633i	−0.0140219	−	0.0704929i
$399$	11.7464	−	0.477532i	0.588057	−	0.0239065i
$400$	0.173249	−	0.418259i	0.00866244	−	0.0209130i
$401$	−5.17012	−	1.75502i	−0.258183	−	0.0876414i	0.189347	−	0.981910i	$-0.439363\pi$
$401$	−5.17012	−	1.75502i	−0.258183	−	0.0876414i	−0.447530	+	0.894269i	$0.647696\pi$
$402$	0.783332	−	11.9513i	0.0390691	−	0.596079i
$403$	−8.23139	+	2.79418i	−0.410035	+	0.139188i
$404$	−3.69055	−	13.7733i	−0.183612	−	0.685248i
$405$	−3.58478	+	2.39527i	−0.178129	+	0.119022i
$406$	2.30378	+	7.38389i	0.114335	+	0.366456i
$407$		−	12.8026i		−	0.634600i
$408$	11.6724	−	0.672071i	0.577868	−	0.0332725i
$409$	−21.3111	+	12.3039i	−1.05376	+	0.608391i	−0.923701	−	0.383115i	$-0.874851\pi$
$409$	−21.3111	+	12.3039i	−1.05376	+	0.608391i	−0.130064	+	0.991506i	$0.541518\pi$
$410$	6.79450	−	8.85476i	0.335556	−	0.437306i
$411$	10.4865	−	0.687321i	0.517260	−	0.0339030i
$412$	−0.667995	−	0.667995i	−0.0329097	−	0.0329097i
$413$	−14.0046	+	13.3261i	−0.689121	+	0.655736i
$414$	−1.49606	−	0.999637i	−0.0735275	−	0.0491295i
$415$	−1.66187	+	4.89570i	−0.0815778	+	0.240320i
$416$	−8.39622	+	1.10538i	−0.411659	+	0.0541959i
$417$	−16.5265	+	2.17575i	−0.809306	+	0.106547i
$418$	−2.90778	+	8.56604i	−0.142224	+	0.418979i
$419$	1.93473	+	1.29275i	0.0945177	+	0.0631547i	0.601931	−	0.798548i	$-0.294398\pi$
$419$	1.93473	+	1.29275i	0.0945177	+	0.0631547i	−0.507413	+	0.861703i	$0.669398\pi$
$420$	−10.1526	+	9.66076i	−0.495396	+	0.471397i
$421$	4.45104	+	4.45104i	0.216930	+	0.216930i	0.807204	−	0.590273i	$-0.200980\pi$
$421$	4.45104	+	4.45104i	0.216930	+	0.216930i	−0.590273	+	0.807204i	$0.700980\pi$
$422$	−14.6808	+	0.962232i	−0.714652	+	0.0468407i
$423$	−2.34612	+	3.05753i	−0.114072	+	0.148662i
$424$	27.5157	−	15.8862i	1.33628	−	0.771501i
$425$	28.3964	−	48.2948i	1.37743	−	2.34264i
$426$			10.8324i			0.524832i
$427$	−1.10650	−	3.54646i	−0.0535472	−	0.171625i
$428$	−13.1396	+	8.77961i	−0.635127	+	0.424379i
$429$	−0.900499	−	3.36071i	−0.0434765	−	0.162257i
$430$	28.2739	−	9.59771i	1.36349	−	0.462843i
$431$	1.74127	−	26.5667i	0.0838742	−	1.27967i	−0.723786	−	0.690024i	$-0.757600\pi$
$431$	1.74127	−	26.5667i	0.0838742	−	1.27967i	0.807660	−	0.589648i	$-0.200734\pi$
$432$	−0.0315497	−	0.0107097i	−0.00151793	−	0.000515269i
$433$	−11.4555	+	27.6560i	−0.550516	+	1.32906i	0.366576	+	0.930388i	$0.380530\pi$
$433$	−11.4555	+	27.6560i	−0.550516	+	1.32906i	−0.917092	+	0.398675i	$0.869470\pi$
$434$	−13.4464	+	0.546641i	−0.645447	+	0.0262396i
$435$	−2.79976	−	14.0753i	−0.134238	−	0.674861i
$436$	−3.42519	−	6.94559i	−0.164037	−	0.332633i
$437$	−2.92604	−	8.61983i	−0.139971	−	0.412342i
$438$	0.547293	−	2.04252i	0.0261507	−	0.0975956i
$439$	−1.16609	−	17.7911i	−0.0556544	−	0.849121i	−0.930861	−	0.365373i	$-0.880942\pi$
$439$	−1.16609	−	17.7911i	−0.0556544	−	0.849121i	0.875207	−	0.483749i	$-0.160725\pi$
$440$	−10.8447	−	26.1814i	−0.517000	−	1.24815i
$441$	−6.59211	+	2.35460i	−0.313910	+	0.112124i
$442$	5.43535	+	0.0431328i	0.258533	+	0.00205162i
$443$	−8.26160	+	14.3095i	−0.392521	+	0.679866i	−0.992781	−	0.119939i	$-0.961730\pi$
$443$	−8.26160	+	14.3095i	−0.392521	+	0.679866i	0.600261	+	0.799804i	$0.295063\pi$
$444$	5.38354	+	4.13093i	0.255491	+	0.196045i
$445$	23.4299	+	11.5543i	1.11068	+	0.547728i
$446$	−4.98680	+	1.33621i	−0.236132	+	0.0632713i
$447$	−3.35939	+	16.8888i	−0.158894	+	0.798812i
$448$	−13.1262	−	2.06067i	−0.620153	−	0.0973576i
$449$	−24.3804	+	4.84957i	−1.15058	+	0.228865i	−0.733296	−	0.679909i	$-0.762019\pi$
$449$	−24.3804	+	4.84957i	−1.15058	+	0.228865i	−0.417287	+	0.908775i	$0.637019\pi$
$450$	−9.46801	+	7.26506i	−0.446326	+	0.342478i
$451$	−0.891790	−	6.77381i	−0.0419927	−	0.318966i
$452$	−11.6533	+	10.2196i	−0.548124	+	0.480692i
$453$	−12.2901	+	6.06080i	−0.577439	+	0.284761i
$454$	13.0030	+	2.58646i	0.610262	+	0.121389i
$455$	−13.1489	+	10.9661i	−0.616428	+	0.514099i
$456$	−7.00016	−	10.4765i	−0.327812	−	0.490606i
$457$	2.65086	−	20.1353i	0.124002	−	0.941887i	−0.810452	−	0.585804i	$-0.800779\pi$
$457$	2.65086	−	20.1353i	0.124002	−	0.941887i	0.934454	−	0.356083i	$-0.115888\pi$
$458$	2.97943	+	5.16053i	0.139220	+	0.241136i
$459$	−3.68331	−	1.85289i	−0.171922	−	0.0864855i
$460$	9.39775	+	5.42579i	0.438172	+	0.252979i
$461$	−23.4974	+	9.73293i	−1.09438	+	0.453308i	−0.855532	−	0.517749i	$-0.826770\pi$
$461$	−23.4974	+	9.73293i	−1.09438	+	0.453308i	−0.238849	+	0.971057i	$0.576770\pi$
$462$	0.133670	−	5.38470i	0.00621887	−	0.250519i
$463$	26.1653	−	26.1653i	1.21600	−	1.21600i	0.246985	−	0.969019i	$-0.420560\pi$
$463$	26.1653	−	26.1653i	1.21600	−	1.21600i	0.969019	−	0.246985i	$-0.0794399\pi$
$464$	0.0731239	−	0.0833819i	0.00339469	−	0.00387091i
$465$	24.9150	+	1.63302i	1.15541	+	0.0757293i
$466$	3.90948	+	4.45791i	0.181103	+	0.206509i
$467$	−0.594363	−	0.774589i	−0.0275038	−	0.0358437i	0.779399	−	0.626528i	$-0.215525\pi$
$467$	−0.594363	−	0.774589i	−0.0275038	−	0.0358437i	−0.806903	+	0.590684i	$0.798858\pi$
$468$	1.70375	+	0.705717i	0.0787560	+	0.0326218i
$469$	−14.6299	+	32.9800i	−0.675546	+	1.52288i
$470$	−8.10768	+	12.1340i	−0.373979	+	0.559700i
$471$	−10.3298	−	9.05900i	−0.475972	−	0.417417i
$472$	20.0133	+	5.36254i	0.921185	+	0.246831i
$473$	8.08404	−	16.3928i	0.371705	−	0.753742i
$474$	12.2201	+	1.60880i	0.561287	+	0.0738948i
$475$	−60.3767			−2.77027
$476$	−12.8253	−	3.89092i	−0.587846	−	0.178340i
$477$	−11.2046			−0.513023
$478$	−18.6338	−	2.45319i	−0.852290	−	0.112206i
$479$	−4.81642	+	9.76674i	−0.220068	+	0.446254i	−0.978708	−	0.205256i	$-0.934197\pi$
$479$	−4.81642	+	9.76674i	−0.220068	+	0.446254i	0.758640	+	0.651510i	$0.225864\pi$
$480$	23.4961	+	6.29576i	1.07245	+	0.287361i
$481$	6.23294	+	5.46614i	0.284197	+	0.249234i
$482$	−2.90172	+	4.34274i	−0.132170	+	0.197806i
$483$	3.19187	+	4.38068i	0.145235	+	0.199328i
$484$	6.38712	+	2.64563i	0.290323	+	0.120256i
$485$	−9.89198	−	12.8915i	−0.449172	−	0.585372i
$486$	0.579097	+	0.660334i	0.0262684	+	0.0299534i
$487$	−9.62281	−	0.630712i	−0.436051	−	0.0285803i	−0.154203	−	0.988039i	$-0.549281\pi$
$487$	−9.62281	−	0.630712i	−0.436051	−	0.0285803i	−0.281848	+	0.959459i	$0.590948\pi$
$488$	−2.62533	+	2.99361i	−0.118843	+	0.135515i
$489$	8.41191	−	8.41191i	0.380400	−	0.380400i
$490$	−24.3253	+	10.5295i	−1.09891	+	0.475675i
$491$	−13.5769	+	5.62373i	−0.612716	+	0.253795i	−0.667389	−	0.744709i	$-0.732588\pi$
$491$	−13.5769	+	5.62373i	−0.612716	+	0.253795i	0.0546734	+	0.998504i	$0.482588\pi$
$492$	3.13617	+	1.81067i	0.141389	+	0.0816312i
$493$	10.3900	−	8.96697i	0.467944	−	0.403852i
$494$	−2.92889	−	5.07298i	−0.131777	−	0.228244i
$495$	−1.30443	+	9.90815i	−0.0586299	+	0.445338i
$496$	0.107199	+	0.160435i	0.00481339	+	0.00720375i
$497$	11.2526	−	30.6299i	0.504749	−	1.37394i
$498$	1.03298	+	0.205473i	0.0462891	+	0.00920748i
$499$	−4.55082	+	2.24422i	−0.203723	+	0.100465i	−0.541288	−	0.840837i	$-0.682063\pi$
$499$	−4.55082	+	2.24422i	−0.203723	+	0.100465i	0.337566	+	0.941302i	$0.390397\pi$
$500$	34.2013	−	29.9937i	1.52953	−	1.34136i
$501$	−2.17752	−	16.5399i	−0.0972844	−	0.738948i
$502$	−7.56843	+	5.80746i	−0.337795	+	0.259200i
$503$	11.2182	−	2.23143i	0.500193	−	0.0994947i	0.0614557	−	0.998110i	$-0.480426\pi$
$503$	11.2182	−	2.23143i	0.500193	−	0.0994947i	0.438738	+	0.898615i	$0.355426\pi$
$504$	5.83691	+	4.71350i	0.259997	+	0.209956i
$505$	−9.76189	+	49.0763i	−0.434398	+	2.18387i
$506$	−4.02861	+	1.07946i	−0.179094	+	0.0479880i
$507$	−9.63871	−	4.75328i	−0.428070	−	0.211101i
$508$	−1.90416	−	1.46111i	−0.0844833	−	0.0648263i
$509$	4.76797	−	8.25837i	0.211337	−	0.366046i	−0.740796	−	0.671730i	$-0.765552\pi$
$509$	4.76797	−	8.25837i	0.211337	−	0.366046i	0.952133	+	0.305684i	$0.0988850\pi$
$510$	−14.3764	−	6.08900i	−0.636598	−	0.269625i
$511$	−3.66929	+	5.20694i	−0.162320	+	0.230342i
$512$	0.144247	+	0.348244i	0.00637489	+	0.0153904i
$513$	0.290612	+	4.43389i	0.0128309	+	0.195761i
$514$	−6.00170	+	22.3987i	−0.264724	+	0.987963i
$515$	1.06559	+	3.13913i	0.0469555	+	0.138327i
$516$	4.28482	+	8.68876i	0.188629	+	0.382501i
$517$	1.74280	+	8.76165i	0.0766483	+	0.385337i
$518$	6.86340	+	10.8451i	0.301560	+	0.476506i
$519$	−3.31259	+	7.99730i	−0.145406	+	0.351042i
$520$	17.3766	+	5.89857i	0.762016	+	0.258669i
$521$	0.0313237	−	0.477908i	0.00137232	−	0.0209375i	−0.997118	−	0.0758683i	$-0.975827\pi$
$521$	0.0313237	−	0.477908i	0.00137232	−	0.0209375i	0.998490	+	0.0549308i	$0.0174938\pi$
$522$	−2.76838	+	0.939738i	−0.121169	+	0.0411312i
$523$	3.79939	+	14.1795i	0.166136	+	0.620027i	0.997893	+	0.0648868i	$0.0206686\pi$
$523$	3.79939	+	14.1795i	0.166136	+	0.620027i	−0.831757	+	0.555140i	$0.812665\pi$
$524$	−7.09276	+	4.73923i	−0.309849	+	0.207034i
$525$	34.3187	−	10.7075i	1.49779	−	0.467313i
$526$		−	7.14474i		−	0.311525i
$527$	10.3908	+	21.4988i	0.452629	+	0.936503i
$528$	−0.0668830	+	0.0386149i	−0.00291071	+	0.00168050i
$529$	−11.4466	+	14.9175i	−0.497678	+	0.648586i
$530$	−42.3369	+	2.77491i	−1.83900	+	0.120534i
$531$	−5.16661	−	5.16661i	−0.224212	−	0.224212i
$532$	3.39092	+	14.0400i	0.147015	+	0.608710i
$533$	3.67859	+	2.45796i	0.159337	+	0.106466i
$534$	1.71065	−	5.03941i	0.0740270	−	0.218077i
$535$	54.9804	−	7.23831i	2.37701	−	0.312939i
$536$	38.3381	−	5.04731i	1.65595	−	0.218011i
$537$	0.149596	−	0.440695i	0.00645554	−	0.0190174i
$538$	−14.8279	−	9.90769i	−0.639277	−	0.427151i
$539$	−5.97155	+	15.0870i	−0.257213	+	0.649843i
$540$	−3.74553	−	3.74553i	−0.161182	−	0.161182i
$541$	3.64982	−	0.239222i	0.156918	−	0.0102850i	0.0132585	−	0.999912i	$-0.495780\pi$
$541$	3.64982	−	0.239222i	0.156918	−	0.0102850i	0.143660	+	0.989627i	$0.454113\pi$
$542$	6.42233	−	8.36975i	0.275863	−	0.359512i
$543$	−0.0945831	+	0.0546076i	−0.00405895	+	0.00234344i
$544$	5.84234	+	22.5172i	0.250488	+	0.965415i
$545$			27.1757i			1.16408i
$546$	2.56448	+	2.36411i	0.109749	+	0.101175i
$547$	−10.7602	+	7.18974i	−0.460073	+	0.307411i	−0.763921	−	0.645310i	$-0.776728\pi$
$547$	−10.7602	+	7.18974i	−0.460073	+	0.307411i	0.303848	+	0.952720i	$0.401728\pi$
$548$	3.34172	+	12.4715i	0.142751	+	0.532754i
$549$	1.32964	−	0.451353i	0.0567478	−	0.0192633i
$550$	−1.80925	+	27.6038i	−0.0771467	+	1.17703i
$551$	−14.0056	−	4.75427i	−0.596660	−	0.202539i
$552$	2.22310	−	5.36703i	0.0946212	−	0.228436i
$553$	−32.8824	−	17.2432i	−1.39830	−	0.733254i
$554$	5.33048	+	26.7981i	0.226471	+	1.13854i
$555$	−10.5320	−	21.3567i	−0.447058	−	0.906543i
$556$	−6.58300	−	19.3929i	−0.279181	−	0.822441i
$557$	0.597234	−	2.22891i	0.0253056	−	0.0944418i	−0.952118	−	0.305731i	$-0.901099\pi$
$557$	0.597234	−	2.22891i	0.0253056	−	0.0944418i	0.977424	+	0.211289i	$0.0677660\pi$
$558$	−0.332670	−	5.07556i	−0.0140830	−	0.214866i
$559$	4.52932	+	10.9347i	0.191570	+	0.462490i
$560$	0.310663	+	0.218922i	0.0131279	+	0.00925113i
$561$	−8.85849	+	3.58722i	−0.374006	+	0.151452i
$562$	−0.754789	+	1.30733i	−0.0318389	+	0.0551465i
$563$	14.8813	+	11.4188i	0.627173	+	0.481247i	0.872774	−	0.488124i	$-0.162319\pi$
$563$	14.8813	+	11.4188i	0.627173	+	0.481247i	−0.245601	+	0.969371i	$0.578985\pi$
$564$	−4.24665	−	2.09422i	−0.178816	−	0.0881825i
$565$	52.5375	−	14.0774i	2.21027	−	0.592240i
$566$	−4.18414	+	21.0351i	−0.175872	+	0.884170i
$567$	−0.951514	−	2.46873i	−0.0399598	−	0.103677i
$568$	−34.3016	+	6.82301i	−1.43926	+	0.286287i
$569$	4.26113	−	3.26968i	0.178636	−	0.137072i	−0.515573	−	0.856846i	$-0.672421\pi$
$569$	4.26113	−	3.26968i	0.178636	−	0.137072i	0.694209	+	0.719773i	$0.255754\pi$
$570$	2.19618	+	16.6816i	0.0919877	+	0.698716i
$571$	−19.0378	+	16.6957i	−0.796709	+	0.698695i	−0.957544	−	0.288286i	$-0.906915\pi$
$571$	−19.0378	+	16.6957i	−0.796709	+	0.698695i	0.160835	+	0.986981i	$0.448581\pi$
$572$	3.83381	−	1.89063i	0.160300	−	0.0790510i
$573$	19.5805	+	3.89480i	0.817987	+	0.162708i
$574$	4.38685	+	5.26003i	0.183103	+	0.219549i
$575$	−15.4653	−	23.1454i	−0.644947	−	0.965231i
$576$	0.655501	−	4.97903i	0.0273126	−	0.207460i
$577$	−2.29860	−	3.98128i	−0.0956918	−	0.165743i	0.814205	−	0.580577i	$-0.197173\pi$
$577$	−2.29860	−	3.98128i	−0.0956918	−	0.165743i	−0.909897	+	0.414834i	$0.863840\pi$
$578$	−1.71370	−	14.8323i	−0.0712807	−	0.616941i
$579$	−21.5039	−	12.4153i	−0.893671	−	0.515961i
$580$	16.2897	−	6.74741i	0.676393	−	0.280171i
$581$	−2.70743	−	1.65405i	−0.112323	−	0.0686217i
$582$	−2.34069	+	2.34069i	−0.0970247	+	0.0970247i
$583$	−17.1245	+	19.5267i	−0.709224	+	0.808715i
$584$	6.81251	+	0.446516i	0.281904	+	0.0184770i
$585$	−4.26685	−	4.86541i	−0.176413	−	0.201160i
$586$	15.3301	+	19.9786i	0.633281	+	0.825308i
$587$	−23.3876	−	9.68745i	−0.965309	−	0.399844i	−0.156345	−	0.987703i	$-0.549971\pi$
$587$	−23.3876	−	9.68745i	−0.965309	−	0.399844i	−0.808964	+	0.587859i	$0.799971\pi$
$588$	−4.41735	−	7.37910i	−0.182168	−	0.304309i
$589$	14.2965	−	21.3963i	0.589079	−	0.881619i
$590$	−20.8018	−	18.2427i	−0.856395	−	0.751038i
$591$	−26.1164	−	6.99787i	−1.07429	−	0.287854i
$592$	0.0813900	−	0.165043i	0.00334511	−	0.00678321i
$593$	7.23572	+	0.952600i	0.297135	+	0.0391186i	0.277620	−	0.960691i	$-0.410454\pi$
$593$	7.23572	+	0.952600i	0.297135	+	0.0391186i	0.0195153	+	0.999810i	$0.493788\pi$
$594$	2.03585			0.0835321
$595$	34.3257	+	32.1514i	1.40722	+	1.31808i
$596$	−21.1562			−0.866591
$597$	−1.61861	−	0.213095i	−0.0662454	−	0.00872138i
$598$	1.19451	−	2.42222i	0.0488469	−	0.0990518i
$599$	23.8061	+	6.37883i	0.972692	+	0.260632i	0.709964	−	0.704238i	$-0.248711\pi$
$599$	23.8061	+	6.37883i	0.972692	+	0.260632i	0.262728	+	0.964870i	$0.415378\pi$
$600$	−28.9689	−	25.4051i	−1.18265	−	1.03716i
$601$	14.5208	−	21.7320i	0.592317	−	0.886465i	−0.407323	−	0.913284i	$-0.633538\pi$
$601$	14.5208	−	21.7320i	0.592317	−	0.886465i	0.999640	+	0.0268188i	$0.00853772\pi$
$602$	1.94010	+	18.2202i	0.0790725	+	0.742600i
$603$	−12.5987	−	5.21854i	−0.513057	−	0.212515i
$604$	−10.2491	−	13.3568i	−0.417028	−	0.543482i
$605$	−15.9958	−	18.2397i	−0.650322	−	0.741550i
$606$	10.1716	+	0.666683i	0.413194	+	0.0270821i
$607$	11.0686	−	12.6214i	0.449262	−	0.512285i	−0.482231	−	0.876044i	$-0.660173\pi$
$607$	11.0686	−	12.6214i	0.449262	−	0.512285i	0.931493	+	0.363759i	$0.118507\pi$
$608$	17.7271	−	17.7271i	0.718928	−	0.718928i
$609$	8.80409	+	0.218552i	0.356760	+	0.00885618i
$610$	4.91232	−	2.03475i	0.198894	−	0.0823846i
$611$	−5.00971	−	2.89236i	−0.202671	−	0.117012i
$612$	1.34988	−	4.88250i	0.0545656	−	0.197364i
$613$	−7.68598	−	13.3125i	−0.310434	−	0.537687i	0.668022	−	0.744141i	$-0.267141\pi$
$613$	−7.68598	−	13.3125i	−0.310434	−	0.537687i	−0.978456	+	0.206454i	$0.933808\pi$
$614$	−0.670358	+	5.09187i	−0.0270534	+	0.205491i
$615$	−7.06010	−	10.5662i	−0.284691	−	0.426070i
$616$	17.1352	−	2.96839i	0.690398	−	0.119600i
$617$	42.3329	+	8.42053i	1.70426	+	0.338998i	0.948722	−	0.316110i	$-0.102377\pi$
$617$	42.3329	+	8.42053i	1.70426	+	0.338998i	0.755535	+	0.655108i	$0.227377\pi$
$618$	0.605682	−	0.298689i	0.0243641	−	0.0120150i
$619$	−28.6690	+	25.1421i	−1.15231	+	1.01054i	−0.152553	+	0.988295i	$0.548749\pi$
$619$	−28.6690	+	25.1421i	−1.15231	+	1.01054i	−0.999752	+	0.0222491i	$0.992917\pi$
$620$	4.00407	+	30.4140i	0.160808	+	1.22145i
$621$	−1.62529	+	1.24713i	−0.0652208	+	0.0500457i
$622$	−2.98353	+	0.593461i	−0.119629	+	0.0237956i
$623$	−10.0719	+	12.4725i	−0.403524	+	0.499700i
$624$	0.00975644	−	0.0490489i	0.000390570	−	0.00196353i
$625$	−88.5680	+	23.7317i	−3.54272	+	0.949269i
$626$	−1.86657	−	0.920491i	−0.0746032	−	0.0367902i
$627$	8.17129	+	6.27005i	0.326330	+	0.250402i
$628$	8.44013	−	14.6187i	0.336798	−	0.583351i
$629$	12.8016	−	18.8338i	0.510435	−	0.750951i
$630$	−4.20672	−	9.09252i	−0.167600	−	0.362255i
$631$	6.48322	+	15.6519i	0.258093	+	0.623091i	0.998812	−	0.0487233i	$-0.0155153\pi$
$631$	6.48322	+	15.6519i	0.258093	+	0.623091i	−0.740720	+	0.671814i	$0.765515\pi$
$632$	2.60267	+	39.7090i	0.103529	+	1.57954i
$633$	−4.33550	+	16.1803i	−0.172321	+	0.643110i
$634$	−1.39881	−	4.12075i	−0.0555537	−	0.163656i
$635$	3.72516	+	7.55388i	0.147829	+	0.299767i
$636$	−2.68562	−	13.5015i	−0.106492	−	0.535370i
$637$	−4.79552	−	9.34874i	−0.190006	−	0.370411i
$638$	−2.59332	+	6.26082i	−0.102670	+	0.247868i
$639$	11.6790	+	3.96448i	0.462013	+	0.156832i
$640$	−1.93812	+	29.5700i	−0.0766110	+	1.16886i
$641$	−4.59426	+	1.55954i	−0.181462	+	0.0615982i	−0.410692	−	0.911774i	$-0.634713\pi$
$641$	−4.59426	+	1.55954i	−0.181462	+	0.0615982i	0.229229	+	0.973372i	$0.426379\pi$
$642$	−2.92387	−	10.9120i	−0.115396	−	0.430664i
$643$	35.9446	−	24.0174i	1.41752	−	0.947154i	0.418271	−	0.908322i	$-0.362636\pi$
$643$	35.9446	−	24.0174i	1.41752	−	0.947154i	0.999246	−	0.0388320i	$-0.0123637\pi$
$644$	−4.51366	+	4.89620i	−0.177863	+	0.192937i
$645$		−	33.9962i		−	1.33860i
$646$	−12.8430	+	9.69387i	−0.505303	+	0.381400i
$647$	30.2566	−	17.4686i	1.18951	−	0.686763i	0.231314	−	0.972879i	$-0.425698\pi$
$647$	30.2566	−	17.4686i	1.18951	−	0.686763i	0.958195	+	0.286116i	$0.0923642\pi$
$648$	−1.72624	+	2.24968i	−0.0678130	+	0.0883756i
$649$	−16.9005	+	1.10771i	−0.663401	+	0.0434816i
$650$	−12.6665	−	12.6665i	−0.496820	−	0.496820i
$651$	−4.33178	+	14.6973i	−0.169776	+	0.576032i
$652$	12.1526	+	8.12009i	0.475932	+	0.318007i
$653$	8.72806	−	25.7120i	0.341556	−	1.00619i	−0.631452	−	0.775415i	$-0.717541\pi$
$653$	8.72806	−	25.7120i	0.341556	−	1.00619i	0.973007	−	0.230775i	$-0.0741261\pi$
$654$	5.48874	−	0.722607i	0.214627	−	0.0282562i
$655$	29.6784	−	3.90724i	1.15963	−	0.152668i
$656$	0.0315669	−	0.0929932i	0.00123248	−	0.00363077i
$657$	−2.00185	−	1.33759i	−0.0780996	−	0.0521845i
$658$	−6.17341	−	6.48771i	−0.240665	−	0.252917i
$659$	34.2605	+	34.2605i	1.33460	+	1.33460i	0.901202	+	0.433399i	$0.142686\pi$
$659$	34.2605	+	34.2605i	1.33460	+	1.33460i	0.433399	+	0.901202i	$0.357314\pi$
$660$	−12.2520	+	0.803036i	−0.476907	+	0.0312581i
$661$	−13.4998	+	17.5933i	−0.525082	+	0.684301i	−0.978322	−	0.207088i	$-0.933601\pi$
$661$	−13.4998	+	17.5933i	−0.525082	+	0.684301i	0.453240	+	0.891389i	$0.350268\pi$
$662$	7.62685	−	4.40336i	0.296426	−	0.171142i
$663$	2.03575	−	5.84435i	0.0790620	−	0.226976i
$664$			3.40044i			0.131962i
$665$	11.1188	−	49.4505i	0.431168	−	1.91761i
$666$	−4.03342	+	2.69504i	−0.156292	+	0.104431i
$667$	−1.76494	−	6.58686i	−0.0683389	−	0.255044i
$668$	19.4086	−	6.58834i	0.750942	−	0.254910i
$669$	−0.384449	+	5.86555i	−0.0148636	+	0.226775i
$670$	−48.8969	−	16.5982i	−1.88905	−	0.641246i
$671$	1.24556	−	3.00705i	0.0480844	−	0.116086i
$672$	−6.93245	+	13.2201i	−0.267425	+	0.509975i
$673$	3.25139	+	16.3458i	0.125332	+	0.630086i	0.991476	+	0.130291i	$0.0415912\pi$
$673$	3.25139	+	16.3458i	0.125332	+	0.630086i	−0.866144	+	0.499795i	$0.833409\pi$
$674$	−3.42275	−	6.94065i	−0.131839	−	0.267344i
$675$	4.36770	+	12.8668i	0.168113	+	0.495244i
$676$	3.41741	−	12.7539i	0.131439	−	0.490536i
$677$	−0.806986	−	12.3122i	−0.0310150	−	0.473197i	−0.984911	−	0.173061i	$-0.944634\pi$
$677$	−0.806986	−	12.3122i	−0.0310150	−	0.473197i	0.953896	−	0.300137i	$-0.0970323\pi$
$678$	−4.24022	−	10.2368i	−0.162845	−	0.393142i
$679$	9.05005	−	4.18707i	0.347309	−	0.160685i
$680$	10.2260	−	49.3591i	0.392148	−	1.89284i
$681$	7.54748	−	13.0726i	0.289220	−	0.500944i
$682$	−9.35384	−	7.17745i	−0.358177	−	0.274839i
$683$	−36.0722	−	17.7888i	−1.38026	−	0.680670i	−0.407658	−	0.913135i	$-0.633654\pi$
$683$	−36.0722	−	17.7888i	−1.38026	−	0.680670i	−0.972605	+	0.232464i	$0.925321\pi$
$684$	−5.27317	+	1.41294i	−0.201625	+	0.0540252i
$685$	8.83919	−	44.4376i	0.337728	−	1.69787i
$686$	−3.02956	−	15.9816i	−0.115669	−	0.610179i
$687$	6.65425	−	1.32361i	0.253875	−	0.0504990i
$688$	0.208429	−	0.159933i	0.00794628	−	0.00609739i
$689$	−2.19519	−	16.6741i	−0.0836302	−	0.635234i
$690$	−5.83236	+	5.11484i	−0.222034	+	0.194719i
$691$	25.3556	−	12.5040i	0.964573	−	0.475675i	0.109389	−	0.993999i	$-0.465111\pi$
$691$	25.3556	−	12.5040i	0.964573	−	0.475675i	0.855184	+	0.518324i	$0.173444\pi$
$692$	−10.4307	−	2.07480i	−0.396516	−	0.0788720i
$693$	−5.75661	−	2.11483i	−0.218675	−	0.0803356i
$694$	−1.84505	−	2.76131i	−0.0700370	−	0.104818i
$695$	−9.38048	+	71.2519i	−0.355822	+	2.70274i
$696$	−4.71946	−	8.17435i	−0.178891	−	0.309848i
$697$	5.46142	−	10.8566i	0.206866	−	0.411224i
$698$	23.4810	+	13.5568i	0.888769	+	0.513131i
$699$	6.23710	−	2.58349i	0.235909	−	0.0977166i
$700$	21.1283	+	38.7875i	0.798575	+	1.46603i
$701$	−2.65433	+	2.65433i	−0.100253	+	0.100253i	−0.755454	−	0.655201i	$-0.772584\pi$
$701$	−2.65433	+	2.65433i	−0.100253	+	0.100253i	0.655201	+	0.755454i	$0.272584\pi$
$702$	−0.869221	+	0.991157i	−0.0328066	+	0.0374088i
$703$	−24.4891	−	1.60510i	−0.923625	−	0.0605376i
$704$	−7.67534	−	8.75205i	−0.289275	−	0.329855i
$705$	10.1150	+	13.1821i	0.380953	+	0.496468i
$706$	9.99575	+	4.14037i	0.376195	+	0.155825i
$707$	−28.0688	−	12.4513i	−1.05564	−	0.468279i
$708$	4.98738	−	7.46414i	0.187437	−	0.280519i
$709$	21.7806	+	19.1011i	0.817987	+	0.717355i	0.962245	−	0.272185i	$-0.0877463\pi$
$709$	21.7806	+	19.1011i	0.817987	+	0.717355i	−0.144258	+	0.989540i	$0.546080\pi$
$710$	45.1112	+	12.0875i	1.69299	+	0.453636i
$711$	6.20687	−	12.5863i	0.232776	−	0.472023i
$712$	17.0351	+	2.24272i	0.638418	+	0.0840494i
$713$	11.8643			0.444321
$714$	5.58096	−	7.78774i	0.208862	−	0.291449i
$715$	−15.0004			−0.560983
$716$	0.566894	+	0.0746330i	0.0211858	+	0.00278916i
$717$	−9.46456	+	19.1922i	−0.353461	+	0.716747i
$718$	2.46863	+	0.661467i	0.0921284	+	0.0246857i
$719$	−4.37797	−	3.83938i	−0.163271	−	0.143185i	0.573812	−	0.818987i	$-0.305464\pi$
$719$	−4.37797	−	3.83938i	−0.163271	−	0.143185i	−0.737083	+	0.675802i	$0.763797\pi$
$720$	−0.0798052	+	0.119437i	−0.00297417	+	0.00445115i
$721$	−2.02291	+	0.215401i	−0.0753371	+	0.00802194i
$722$	0.603564	+	0.250004i	0.0224623	+	0.00930419i
$723$	3.62014	+	4.71786i	0.134635	+	0.175459i
$724$	−0.0884726	−	0.100884i	−0.00328806	−	0.00374931i
$725$	−45.1328	−	2.95816i	−1.67619	−	0.109863i
$726$	−3.25858	+	3.71570i	−0.120937	+	0.137903i
$727$	−7.47838	+	7.47838i	−0.277358	+	0.277358i	−0.832053	−	0.554696i	$-0.812835\pi$
$727$	−7.47838	+	7.47838i	−0.277358	+	0.277358i	0.554696	+	0.832053i	$0.312835\pi$
$728$	−5.87084	+	9.60967i	−0.217588	+	0.356158i
$729$	0.923880	−	0.382683i	0.0342178	−	0.0141735i
$730$	−7.89532	−	4.55836i	−0.292219	−	0.168713i
$731$	28.2840	−	16.0319i	1.04612	−	0.592960i
$732$	0.862580	+	1.49403i	0.0318819	+	0.0552211i
$733$	−6.89970	+	52.4084i	−0.254846	+	1.93575i	0.0874767	+	0.996167i	$0.472120\pi$
$733$	−6.89970	+	52.4084i	−0.254846	+	1.93575i	−0.342323	+	0.939582i	$0.611214\pi$
$734$	12.2139	+	18.2795i	0.450825	+	0.674707i
$735$	2.44976	+	30.0800i	0.0903607	+	1.10952i
$736$	11.3364	+	2.25495i	0.417866	+	0.0831187i
$737$	−28.3497	+	13.9805i	−1.04427	+	0.514979i
$738$	−1.94635	+	1.70690i	−0.0716460	+	0.0628318i
$739$	3.20958	+	24.3792i	0.118066	+	0.896802i	0.943284	+	0.331987i	$0.107719\pi$
$739$	3.20958	+	24.3792i	0.118066	+	0.896802i	−0.825218	+	0.564815i	$0.808948\pi$
$740$	23.2104	−	17.8100i	0.853233	−	0.654708i
$741$	−6.54136	+	1.30116i	−0.240303	+	0.0477992i
$742$	4.03801	−	25.7215i	0.148240	−	0.944267i
$743$	0.190894	−	0.959691i	0.00700324	−	0.0352076i	−0.977126	−	0.212663i	$-0.931786\pi$
$743$	0.190894	−	0.959691i	0.00700324	−	0.0352076i	0.984129	+	0.177455i	$0.0567864\pi$
$744$	15.8626	−	4.25036i	0.581550	−	0.155826i
$745$	66.5842	+	32.8357i	2.43946	+	1.20301i
$746$	−12.3640	−	9.48721i	−0.452677	−	0.347352i
$747$	0.599586	−	1.03851i	0.0219377	−	0.0379972i
$748$	−6.44587	−	9.81465i	−0.235684	−	0.358859i
$749$	−3.06775	+	33.8923i	−0.112093	+	1.23840i
$750$	12.4446	+	30.0440i	0.454414	+	1.09705i
$751$	−1.98385	−	30.2677i	−0.0723917	−	1.10448i	−0.867310	−	0.497768i	$-0.834153\pi$
$751$	−1.98385	−	30.2677i	−0.0723917	−	1.10448i	0.794919	−	0.606716i	$-0.207513\pi$
$752$	−0.0332335	+	0.124029i	−0.00121190	+	0.00452288i
$753$	3.49140	+	10.2853i	0.127234	+	0.374819i
$754$	−1.94085	−	3.93566i	−0.0706816	−	0.143328i
$755$	11.5259	+	57.9447i	0.419471	+	2.10882i
$756$	2.74675	−	1.73830i	0.0998982	−	0.0632213i
$757$	14.7869	−	35.6986i	0.537437	−	1.29749i	−0.389069	−	0.921209i	$-0.627203\pi$
$757$	14.7869	−	35.6986i	0.537437	−	1.29749i	0.926506	−	0.376280i	$-0.122797\pi$
$758$	−6.91182	−	2.34625i	−0.251049	−	0.0852195i
$759$	−0.310579	+	4.73852i	−0.0112733	+	0.171997i
$760$	−51.4402	+	17.4616i	−1.86593	+	0.633398i
$761$	−4.51529	−	16.8513i	−0.163679	−	0.610859i	−0.998205	−	0.0598902i	$-0.980925\pi$
$761$	−4.51529	−	16.8513i	−0.163679	−	0.610859i	0.834526	−	0.550969i	$-0.185742\pi$
$762$	1.42662	−	0.953237i	0.0516810	−	0.0345321i
$763$	−16.2707	−	3.65840i	−0.589038	−	0.132443i
$764$			24.5280i			0.887392i
$765$	−11.8264	+	13.2715i	−0.427584	+	0.479831i
$766$	6.41315	−	3.70263i	0.231717	−	0.133782i
$767$	6.67647	−	8.70094i	0.241073	−	0.314173i
$768$	16.0463	−	1.05173i	0.579022	−	0.0379511i
$769$	−5.72791	−	5.72791i	−0.206554	−	0.206554i	0.596247	−	0.802801i	$-0.296658\pi$
$769$	−5.72791	−	5.72791i	−0.206554	−	0.206554i	−0.802801	+	0.596247i	$0.796658\pi$
$770$	−22.2753	−	6.56527i	−0.802745	−	0.236596i
$771$	21.9526	+	14.6683i	0.790604	+	0.528265i
$772$	9.80614	−	28.8880i	0.352931	−	1.03970i
$773$	−14.3266	+	1.88613i	−0.515292	+	0.0678395i	−0.383688	−	0.923463i	$-0.625346\pi$
$773$	−14.3266	+	1.88613i	−0.515292	+	0.0678395i	−0.131604	+	0.991302i	$0.542013\pi$
$774$	−6.86628	+	0.903962i	−0.246803	+	0.0324923i
$775$	25.2947	−	74.5157i	0.908612	−	2.67668i
$776$	−8.88628	−	5.93762i	−0.318999	−	0.213148i
$777$	14.2045	−	3.43066i	0.509585	−	0.123074i
$778$	−1.63861	−	1.63861i	−0.0587469	−	0.0587469i
$779$	−13.0690	+	0.856585i	−0.468244	+	0.0306903i
$780$	4.84010	−	6.30774i	0.173303	−	0.225853i
$781$	24.7586	−	14.2944i	0.885932	−	0.511493i
$782$	−7.00585	−	2.44033i	−0.250529	−	0.0872662i
$783$			3.32866i			0.118957i
$784$	−0.172894	+	0.156529i	−0.00617480	+	0.00559033i
$785$	−49.2526	+	32.9095i	−1.75790	+	1.17459i
$786$	−1.57831	−	5.89032i	−0.0562963	−	0.210101i
$787$	−16.6330	+	5.64615i	−0.592903	+	0.201264i	−0.601733	−	0.798697i	$-0.705523\pi$
$787$	−16.6330	+	5.64615i	−0.592903	+	0.201264i	0.00882953	+	0.999961i	$0.497189\pi$
$788$	2.17260	−	33.1475i	0.0773958	−	1.18083i
$789$	−7.70311	−	2.61485i	−0.274238	−	0.0930912i
$790$	20.3358	−	49.0949i	0.723514	−	1.74672i
$791$	1.35581	+	33.3504i	0.0482069	+	1.18580i
$792$	1.28232	+	6.44667i	0.0455654	+	0.229073i
$793$	0.932184	+	1.89028i	0.0331028	+	0.0671259i
$794$	4.52503	+	13.3303i	0.160587	+	0.473075i
$795$	−12.5028	+	46.6612i	−0.443429	+	1.65490i
$796$	−0.131185	−	2.00150i	−0.00464974	−	0.0709414i
$797$	−16.7731	−	40.4938i	−0.594134	−	1.43437i	−0.879478	−	0.475940i	$-0.842108\pi$
$797$	−16.7731	−	40.4938i	−0.594134	−	1.43437i	0.285344	−	0.958425i	$-0.407892\pi$
$798$	−10.2833	−	0.930786i	−0.364024	−	0.0329495i
$799$	−6.19720	+	14.6319i	−0.219241	+	0.517638i
$800$	38.3319	−	66.3928i	1.35524	−	2.34734i
$801$	−4.80718	−	3.68868i	−0.169853	−	0.130333i
$802$	4.30082	+	2.12093i	0.151867	+	0.0748927i
$803$	−5.39060	+	1.44441i	−0.190230	+	0.0509720i
$804$	3.26857	−	16.4322i	0.115273	−	0.579519i
$805$	21.8049	−	8.40419i	0.768522	−	0.296209i
$806$	7.48803	−	1.48946i	0.263755	−	0.0524640i
$807$	−16.1088	+	12.3607i	−0.567055	+	0.435117i
$808$	4.29569	+	32.6290i	0.151122	+	1.14789i
$809$	12.0120	−	10.5343i	0.422320	−	0.370365i	−0.421646	−	0.906760i	$-0.638548\pi$
$809$	12.0120	−	10.5343i	0.422320	−	0.370365i	0.843967	+	0.536395i	$0.180214\pi$
$810$	3.39613	−	1.67479i	0.119328	−	0.0588460i
$811$	−30.1442	−	5.99606i	−1.05851	−	0.210550i	−0.365006	−	0.931005i	$-0.618933\pi$
$811$	−30.1442	−	5.99606i	−1.05851	−	0.210550i	−0.693502	+	0.720455i	$0.743933\pi$
$812$	1.84689	+	10.6613i	0.0648131	+	0.374138i
$813$	−6.67339	−	9.98743i	−0.234046	−	0.350275i
$814$	−1.46769	+	11.1482i	−0.0514423	+	0.390743i
$815$	−25.6446	−	44.4177i	−0.898290	−	1.55588i
$816$	−0.137003	−	0.0100721i	−0.00479607	−	0.000352594i
$817$	−30.3431	−	17.5186i	−1.06157	−	0.612899i
$818$	19.9677	−	8.27089i	0.698154	−	0.289185i
$819$	3.48742	−	1.89967i	0.121860	−	0.0663798i
$820$	11.0400	−	11.0400i	0.385534	−	0.385534i
$821$	−11.0360	+	12.5842i	−0.385161	+	0.439191i	−0.911636	−	0.410999i	$-0.865180\pi$
$821$	−11.0360	+	12.5842i	−0.385161	+	0.439191i	0.526475	+	0.850190i	$0.323513\pi$
$822$	−9.21019	−	0.603668i	−0.321242	−	0.0210553i
$823$	12.9045	+	14.7148i	0.449824	+	0.512926i	0.931658	−	0.363337i	$-0.118363\pi$
$823$	12.9045	+	14.7148i	0.449824	+	0.512926i	−0.481834	+	0.876262i	$0.660029\pi$
$824$	1.32732	+	1.72980i	0.0462394	+	0.0602604i
$825$	29.0989	+	12.0532i	1.01310	+	0.419638i
$826$	13.7226	−	9.99860i	0.477470	−	0.347896i
$827$	−1.42208	+	2.12829i	−0.0494505	+	0.0740079i	−0.855371	−	0.518016i	$-0.826671\pi$
$827$	−1.42208	+	2.12829i	−0.0494505	+	0.0740079i	0.805921	+	0.592024i	$0.201671\pi$
$828$	−1.89236	−	1.65955i	−0.0657639	−	0.0576734i
$829$	−37.0458	−	9.92639i	−1.28665	−	0.344758i	−0.450265	−	0.892895i	$-0.648670\pi$
$829$	−37.0458	−	9.92639i	−1.28665	−	0.344758i	−0.836388	+	0.548137i	$0.815337\pi$
$830$	2.00836	−	4.07255i	0.0697111	−	0.141360i
$831$	30.8433	+	4.06060i	1.06994	+	0.140861i
$832$	7.53798			0.261332
$833$	−23.8706	+	16.2232i	−0.827068	+	0.562102i
$834$	14.6403			0.506952
$835$	−71.3097	−	9.38810i	−2.46777	−	0.324888i
$836$	−5.59683	+	11.3493i	−0.193570	+	0.392522i
$837$	−5.59397	−	1.49890i	−0.193356	−	0.0518096i
$838$	−1.53652	−	1.34749i	−0.0530781	−	0.0465483i
$839$	19.2605	−	28.8254i	0.664947	−	0.995164i	−0.333675	−	0.942688i	$-0.608289\pi$
$839$	19.2605	−	28.8254i	0.664947	−	0.995164i	0.998622	−	0.0524759i	$-0.0167113\pi$
$840$	26.1424	−	19.0480i	0.901998	−	0.657218i
$841$	16.5559	+	6.85770i	0.570895	+	0.236472i
$842$	−3.36559	−	4.38613i	−0.115986	−	0.151156i
$843$	1.13326	+	1.29224i	0.0390317	+	0.0445071i
$844$	−20.5364	−	1.34603i	−0.706893	−	0.0463322i
$845$	−30.5504	+	34.8361i	−1.05097	+	1.19840i
$846$	2.39346	−	2.39346i	0.0822890	−	0.0822890i
$847$	13.0738	−	7.12157i	0.449222	−	0.244700i
$848$	−0.344896	+	0.142861i	−0.0118438	+	0.00490586i
$849$	21.1477	+	12.2096i	0.725786	+	0.419033i
$850$	−30.2634	+	38.7987i	−1.03803	+	1.33078i
$851$	−5.65749	−	9.79906i	−0.193936	−	0.335907i
$852$	−1.97787	+	15.0234i	−0.0677606	+	0.514693i
$853$	19.5687	+	29.2867i	0.670021	+	1.00276i	0.998306	+	0.0581782i	$0.0185292\pi$
$853$	19.5687	+	29.2867i	0.670021	+	1.00276i	−0.328286	+	0.944579i	$0.606471\pi$
$854$	0.556948	+	3.21502i	0.0190584	+	0.110016i
$855$	18.7891	+	3.73738i	0.642572	+	0.127816i
$856$	32.7121	−	16.1318i	1.11808	−	0.551374i
$857$	32.1984	−	28.2372i	1.09988	−	0.964566i	0.100339	−	0.994953i	$-0.468007\pi$
$857$	32.1984	−	28.2372i	1.09988	−	0.964566i	0.999538	+	0.0303873i	$0.00967406\pi$
$858$	0.398862	+	3.02966i	0.0136169	+	0.103431i
$859$	15.3070	−	11.7455i	0.522267	−	0.400750i	−0.313706	−	0.949520i	$-0.601571\pi$
$859$	15.3070	−	11.7455i	0.522267	−	0.400750i	0.835973	+	0.548770i	$0.184904\pi$
$860$	40.9653	−	8.14851i	1.39691	−	0.277862i
$861$	7.27662	−	2.80460i	0.247987	−	0.0955806i
$862$	−4.56186	+	22.9340i	−0.155378	+	0.781136i
$863$	42.8001	−	11.4682i	1.45693	−	0.390384i	0.558502	−	0.829503i	$-0.311376\pi$
$863$	42.8001	−	11.4682i	1.45693	−	0.390384i	0.898429	+	0.439119i	$0.144709\pi$
$864$	−5.06020	−	2.49541i	−0.172151	−	0.0848957i
$865$	29.6081	+	22.7191i	1.00670	+	0.772472i
$866$	13.1457	−	22.7690i	0.446708	−	0.773721i
$867$	−16.6186	−	3.58073i	−0.564398	−	0.121608i
$868$	−18.7485	−	1.69701i	−0.636365	−	0.0576004i
$869$	−12.4484	−	30.0532i	−0.422284	−	1.01948i
$870$	0.824369	+	12.5774i	0.0279487	+	0.426415i
$871$	5.29766	−	19.7711i	0.179504	−	0.669919i
$872$	5.74537	+	16.9253i	0.194563	+	0.573164i
$873$	1.66696	+	3.38027i	0.0564182	+	0.114405i
$874$	1.55975	+	7.84139i	0.0527593	+	0.265239i
$875$	−3.97916	−	97.8802i	−0.134520	−	3.30896i
$876$	1.13198	−	2.73283i	0.0382459	−	0.0923338i
$877$	43.7722	+	14.8587i	1.47808	+	0.501742i	0.940007	−	0.341154i	$-0.110818\pi$
$877$	43.7722	+	14.8587i	1.47808	+	0.501742i	0.538076	+	0.842896i	$0.319151\pi$
$878$	−1.02416	+	15.6257i	−0.0345639	+	0.527343i
$879$	27.1505	−	9.21635i	0.915764	−	0.310860i
$880$	0.0861781	+	0.321621i	0.00290506	+	0.0108418i
$881$	−2.22626	+	1.48754i	−0.0750045	+	0.0501164i	−0.592507	−	0.805565i	$-0.701862\pi$
$881$	−2.22626	+	1.48754i	−0.0750045	+	0.0501164i	0.517503	+	0.855682i	$0.326862\pi$
$882$	6.01018	−	1.29461i	0.202373	−	0.0435919i
$883$		−	55.7167i		−	1.87501i	−0.347965	−	0.937507i	$-0.613127\pi$
$883$		−	55.7167i		−	1.87501i	0.347965	−	0.937507i	$-0.386873\pi$
$884$	7.53037	+	1.05225i	0.253274	+	0.0353910i
$885$	−27.2814	+	15.7509i	−0.917055	+	0.529462i
$886$	8.83445	−	11.5133i	0.296799	−	0.386796i
$887$	−17.4332	+	1.14263i	−0.585348	+	0.0383657i	−0.355201	−	0.934790i	$-0.615587\pi$
$887$	−17.4332	+	1.14263i	−0.585348	+	0.0383657i	−0.230147	+	0.973156i	$0.573921\pi$
$888$	−11.0746	−	11.0746i	−0.371638	−	0.371638i
$889$	−5.02414	+	1.21342i	−0.168504	+	0.0406970i
$890$	−19.0776	−	12.7472i	−0.639483	−	0.427289i
$891$	0.745088	−	2.19496i	0.0249614	−	0.0735339i
$892$	−7.16013	+	0.942649i	−0.239739	+	0.0315622i
$893$	16.9780	−	2.23520i	0.568149	−	0.0747982i
$894$	4.86141	−	14.3212i	0.162590	−	0.478974i
$895$	−1.66833	−	1.11474i	−0.0557662	−	0.0372618i
$896$	−17.4432	−	5.14111i	−0.582738	−	0.171752i
$897$	−2.17435	−	2.17435i	−0.0725993	−	0.0725993i
$898$	21.7859	−	1.42792i	0.727004	−	0.0476503i
$899$	11.7353	−	15.2937i	0.391393	−	0.510073i
$900$	−14.4576	+	8.34711i	−0.481920	+	0.278237i
$901$	−44.7171	+	11.6024i	−1.48974	+	0.386531i
$902$			6.00071i			0.199802i
$903$	20.3542	+	4.57657i	0.677345	+	0.152299i
$904$	29.7447	−	19.8748i	0.989295	−	0.661026i
$905$	0.121869	+	0.454823i	0.00405108	+	0.0151188i
$906$	11.3967	−	3.86867i	0.378631	−	0.128528i
$907$	0.702563	−	10.7190i	0.0233282	−	0.355920i	−0.970198	−	0.242315i	$-0.922093\pi$
$907$	0.702563	−	10.7190i	0.0233282	−	0.355920i	0.993526	−	0.113605i	$-0.0362400\pi$
$908$	17.5615	+	5.96133i	0.582800	+	0.197834i
$909$	4.44142	−	10.7225i	0.147313	−	0.355644i
$910$	12.7069	−	8.04164i	0.421229	−	0.266578i
$911$	−0.781248	−	3.92760i	−0.0258839	−	0.130127i	0.965683	−	0.259724i	$-0.0836316\pi$
$911$	−0.781248	−	3.92760i	−0.0258839	−	0.130127i	−0.991567	+	0.129597i	$0.958632\pi$
$912$	0.0654784	+	0.132777i	0.00216821	+	0.00439669i
$913$	−0.893488	−	2.63213i	−0.0295701	−	0.0871108i
$914$	−4.61661	+	17.2294i	−0.152704	+	0.569898i
$915$	−0.395942	−	6.04090i	−0.0130894	−	0.199706i
$916$	3.18990	+	7.70110i	0.105397	+	0.254452i
$917$	−1.65597	+	18.2951i	−0.0546850	+	0.604156i
$918$	2.99493	+	2.03571i	0.0988474	+	0.0671884i
$919$	24.0103	−	41.5871i	0.792028	−	1.37183i	−0.132682	−	0.991159i	$-0.542359\pi$
$919$	24.0103	−	41.5871i	0.792028	−	1.37183i	0.924709	−	0.380674i	$-0.124308\pi$
$920$	−19.8701	−	15.2469i	−0.655099	−	0.502675i
$921$	5.24447	+	2.58629i	0.172811	+	0.0852210i
$922$	21.5767	−	5.78147i	0.710592	−	0.190403i
$923$	−3.61162	+	18.1568i	−0.118878	+	0.597639i
$924$	1.16857	−	7.44360i	0.0384430	−	0.244876i
$925$	−73.6065	+	14.6412i	−2.42017	+	0.481401i
$926$	−25.7837	+	19.7845i	−0.847306	+	0.650160i
$927$	−0.100363	−	0.762332i	−0.00329635	−	0.0250383i
$928$	14.1199	−	12.3828i	0.463508	−	0.406486i
$929$	1.97736	−	0.975125i	0.0648750	−	0.0319928i	−0.409562	−	0.912282i	$-0.634318\pi$
$929$	1.97736	−	0.975125i	0.0648750	−	0.0319928i	0.474437	+	0.880290i	$0.342652\pi$
$930$	−21.5082	−	4.27825i	−0.705282	−	0.140289i
$931$	28.1102	+	13.3141i	0.921274	+	0.436351i
$932$	4.60807	+	6.89646i	0.150942	+	0.225901i
$933$	−0.452080	+	3.43389i	−0.0148004	+	0.112421i
$934$	0.428759	+	0.742632i	0.0140294	+	0.0242997i
$935$	5.05397	+	40.8937i	0.165282	+	1.33737i
$936$	−3.68606	−	2.12815i	−0.120483	−	0.0695607i
$937$	25.2421	−	10.4556i	0.824625	−	0.341571i	0.0698522	−	0.997557i	$-0.477747\pi$
$937$	25.2421	−	10.4556i	0.824625	−	0.341571i	0.754773	+	0.655987i	$0.227747\pi$
$938$	16.5202	−	27.0411i	0.539404	−	0.882922i
$939$	−1.67556	+	1.67556i	−0.0546799	+	0.0546799i
$940$	−13.4600	+	15.3482i	−0.439017	+	0.500603i
$941$	25.4871	+	1.67052i	0.830857	+	0.0544572i	0.474894	−	0.880043i	$-0.342486\pi$
$941$	25.4871	+	1.67052i	0.830857	+	0.0544572i	0.355963	+	0.934500i	$0.384153\pi$
$942$	7.95643	+	9.07257i	0.259235	+	0.295600i
$943$	−3.67594	−	4.79058i	−0.119705	−	0.156003i
$944$	−0.224912	−	0.0931617i	−0.00732027	−	0.00303215i
$945$	−11.3427	+	1.20778i	−0.368978	+	0.0392890i
$946$	−8.91867	+	13.3477i	−0.289971	+	0.433972i
$947$	15.1816	+	13.3139i	0.493335	+	0.432643i	0.869517	−	0.493903i	$-0.164430\pi$
$947$	15.1816	+	13.3139i	0.493335	+	0.432643i	−0.376182	+	0.926546i	$0.622763\pi$
$948$	16.6542	+	4.46247i	0.540903	+	0.144934i
$949$	1.59834	−	3.24112i	0.0518844	−	0.105211i
$950$	52.5746	+	6.92158i	1.70575	+	0.224566i
$951$	−4.95473			−0.160668
$952$	28.1757	+	12.7672i	0.913179	+	0.413788i
$953$	0.858738			0.0278172			0.0139086	−	0.999903i	$-0.495573\pi$
$953$	0.858738			0.0278172			0.0139086	+	0.999903i	$0.495573\pi$
$954$	9.75670	+	1.28449i	0.315885	+	0.0415870i
$955$	38.0690	−	77.1963i	1.23188	−	2.49801i
$956$	−25.3952	−	6.80461i	−0.821338	−	0.220077i
$957$	5.80100	+	5.08734i	0.187520	+	0.164450i
$958$	5.31369	−	7.95250i	0.171678	−	0.256934i
$959$	25.4158	+	11.2744i	0.820717	+	0.364069i
$960$	−20.0035	−	8.28574i	−0.645612	−	0.267421i
$961$	1.54578	+	2.01450i	0.0498638	+	0.0649838i
$962$	−4.80086	−	5.47433i	−0.154786	−	0.176499i
$963$	−12.8349	−	0.841245i	−0.413599	−	0.0271087i
$964$	−4.81731	+	5.49309i	−0.155155	+	0.176920i
$965$	−75.6985	+	75.6985i	−2.43682	+	2.43682i
$966$	−2.27721	−	4.18051i	−0.0732679	−	0.134506i
$967$	22.5906	−	9.35731i	0.726463	−	0.300911i	0.0113655	−	0.999935i	$-0.496382\pi$
$967$	22.5906	−	9.35731i	0.726463	−	0.300911i	0.715098	+	0.699025i	$0.246382\pi$
$968$	−13.8185	−	7.97811i	−0.444143	−	0.256426i
$969$	5.75112	+	17.3945i	0.184753	+	0.558793i
$970$	7.13583	+	12.3596i	0.229118	+	0.396843i
$971$	−2.83109	+	21.5043i	−0.0908539	+	0.690104i	0.884036	+	0.467418i	$0.154816\pi$
$971$	−2.83109	+	21.5043i	−0.0908539	+	0.690104i	−0.974890	+	0.222686i	$0.928518\pi$
$972$	0.682577	+	1.02155i	0.0218937	+	0.0327662i
$973$	−41.3971	−	15.2082i	−1.32713	−	0.487553i
$974$	8.30702	+	1.65237i	0.266174	+	0.0529453i
$975$	−18.2921	+	9.02066i	−0.585816	+	0.288892i
$976$	0.0351738	−	0.0308466i	0.00112589	−	0.000987376i
$977$	0.770869	+	5.85533i	0.0246623	+	0.187329i	0.999342	−	0.0362781i	$-0.0115502\pi$
$977$	0.770869	+	5.85533i	0.0246623	+	0.187329i	−0.974679	+	0.223607i	$0.928217\pi$
$978$	−8.28924	+	6.36056i	−0.265061	+	0.203388i
$979$	−13.7755	+	2.74011i	−0.440265	+	0.0875742i
$980$	−35.6592	+	10.1618i	−1.13909	+	0.324607i
$981$	1.22971	−	6.18215i	0.0392615	−	0.197381i
$982$	12.4671	−	3.34056i	0.397842	−	0.106602i
$983$	7.25920	+	3.57984i	0.231532	+	0.114179i	0.554355	−	0.832280i	$-0.312965\pi$
$983$	7.25920	+	3.57984i	0.231532	+	0.114179i	−0.322822	+	0.946460i	$0.604632\pi$
$984$	−6.63096	−	5.08811i	−0.211387	−	0.162203i
$985$	−58.2848	+	100.952i	−1.85711	+	3.21660i
$986$	−10.0754	+	6.61712i	−0.320866	+	0.210732i
$987$	−9.25409	+	4.28148i	−0.294561	+	0.136281i
$988$	−3.13579	−	7.57046i	−0.0997627	−	0.240848i
$989$	−1.05652	−	16.1194i	−0.0335954	−	0.512567i
$990$	2.27174	−	8.47825i	0.0722006	−	0.269456i
$991$	0.516551	+	1.52171i	0.0164088	+	0.0483387i	0.954826	−	0.297165i	$-0.0960413\pi$
$991$	0.516551	+	1.52171i	0.0164088	+	0.0483387i	−0.938417	+	0.345504i	$0.887708\pi$
$992$	14.4517	+	29.3051i	0.458842	+	0.930439i
$993$	−1.95619	−	9.83445i	−0.0620780	−	0.312087i
$994$	−13.3099	+	25.3818i	−0.422165	+	0.805061i
$995$	−2.69358	+	6.50288i	−0.0853922	+	0.206155i
$996$	1.39512	+	0.473579i	0.0442061	+	0.0150059i
$997$	−0.873896	+	13.3331i	−0.0276766	+	0.422263i	0.961429	+	0.275054i	$0.0886957\pi$
$997$	−0.873896	+	13.3331i	−0.0276766	+	0.422263i	−0.989105	+	0.147209i	$0.952971\pi$
$998$	4.22002	−	1.43251i	0.133583	−	0.0453452i
$999$	1.42950	+	5.33497i	0.0452274	+	0.168791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.250.9	yes	384
7.3	odd	6	inner	357.2.bl.a.199.16	yes	384
17.10	odd	16	inner	357.2.bl.a.61.16	yes	384
119.10	even	48	inner	357.2.bl.a.10.9	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.9	✓	384	119.10	even	48	inner
357.2.bl.a.61.16	yes	384	17.10	odd	16	inner
357.2.bl.a.199.16	yes	384	7.3	odd	6	inner
357.2.bl.a.250.9	yes	384	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.870777 - 0.114640i) q^{2} +(-0.442289 + 0.896873i) q^{3} +(-1.18674 - 0.317986i) q^{4} +(3.24146 + 2.84269i) q^{5} +(0.487952 - 0.730272i) q^{6} +(-2.13834 + 1.55805i) q^{7} +(2.61980 + 1.08516i) q^{8} +(-0.608761 - 0.793353i) q^{9} +(-2.49670 - 2.84695i) q^{10} +(-2.31301 - 0.151603i) q^{11} +(0.810076 - 0.923714i) q^{12} +(1.06136 - 1.06136i) q^{13} +(2.04063 - 1.11157i) q^{14} +(-3.98319 + 1.64989i) q^{15} +(-0.0288541 - 0.0166589i) q^{16} +(-3.25106 - 2.53587i) q^{17} +(0.439145 + 0.760622i) q^{18} +(-0.579980 + 4.40539i) q^{19} +(-2.94284 - 4.40428i) q^{20} +(-0.451605 - 2.60692i) q^{21} +(1.99674 + 0.397175i) q^{22} +(-1.83737 + 0.906089i) q^{23} +(-2.13196 + 1.86968i) q^{24} +(1.77358 + 13.4717i) q^{25} +(-1.04588 + 0.802535i) q^{26} +(0.980785 - 0.195090i) q^{27} +(3.03309 - 1.16903i) q^{28} +(-0.649389 + 3.26470i) q^{29} +(3.65761 - 0.980054i) q^{30} +(-5.19406 - 2.56143i) q^{31} +(-4.47614 - 3.43466i) q^{32} +(1.15899 - 2.00742i) q^{33} +(2.54024 + 2.58087i) q^{34} +(-11.3604 - 1.02828i) q^{35} +(0.470167 + 1.13508i) q^{36} +(0.361233 + 5.51135i) q^{37} +(1.01007 - 3.76962i) q^{38} +(0.482478 + 1.42134i) q^{39} +(5.40723 + 10.9648i) q^{40} +(0.575032 + 2.89088i) q^{41} +(0.0943899 + 2.32182i) q^{42} +(-3.01755 + 7.28500i) q^{43} +(2.69674 + 0.915419i) q^{44} +(0.281977 - 4.30214i) q^{45} +(1.70381 - 0.578366i) q^{46} +(-0.997470 - 3.72261i) q^{47} +(0.0277028 - 0.0185104i) q^{48} +(2.14499 - 6.66326i) q^{49} -11.9342i q^{50} +(3.71226 - 1.79420i) q^{51} +(-1.59706 + 0.922064i) q^{52} +(6.82093 - 8.88921i) q^{53} +(-0.876410 + 0.0574430i) q^{54} +(-7.06658 - 7.06658i) q^{55} +(-7.29275 + 1.76134i) q^{56} +(-3.69455 - 2.46862i) q^{57} +(0.939738 - 2.76838i) q^{58} +(7.24418 - 0.953715i) q^{59} +(5.25166 - 0.691394i) q^{60} +(-0.451353 + 1.32964i) q^{61} +(4.22923 + 2.82588i) q^{62} +(2.53782 + 0.747980i) q^{63} +(3.55108 + 3.55108i) q^{64} +(6.45749 - 0.423246i) q^{65} +(-1.23935 + 1.61515i) q^{66} +(11.8097 - 6.81835i) q^{67} +(3.05180 + 4.04321i) q^{68} -2.04864i q^{69} +(9.77447 + 2.19776i) q^{70} +(-10.2549 + 6.85214i) q^{71} +(-0.733921 - 2.73903i) q^{72} +(2.27983 - 0.773899i) q^{73} +(0.317267 - 4.84056i) q^{74} +(-12.8668 - 4.36770i) q^{75} +(2.08914 - 5.04363i) q^{76} +(5.18220 - 3.27960i) q^{77} +(-0.257189 - 1.29298i) q^{78} +(6.20687 + 12.5863i) q^{79} +(-0.0461734 - 0.136022i) q^{80} +(-0.258819 + 0.965926i) q^{81} +(-0.169314 - 2.58323i) q^{82} +(0.458903 + 1.10789i) q^{83} +(-0.293028 + 3.23735i) q^{84} +(-3.32951 - 17.4617i) q^{85} +(3.46276 - 5.99768i) q^{86} +(-2.64080 - 2.02636i) q^{87} +(-5.89512 - 2.90715i) q^{88} +(5.85285 - 1.56827i) q^{89} +(-0.738737 + 3.71388i) q^{90} +(-0.615902 + 3.92320i) q^{91} +(2.46860 - 0.491036i) q^{92} +(4.59455 - 3.52552i) q^{93} +(0.441814 + 3.35591i) q^{94} +(-14.4031 + 12.6312i) q^{95} +(5.06020 - 2.49541i) q^{96} +(-3.69653 - 0.735286i) q^{97} +(-2.63168 + 5.55631i) q^{98} +(1.28780 + 1.92732i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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