LMFDB - Embedded newform 357.2.bl.a.250.21

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			250.21
Character	$\chi$	$=$	357.250
Dual form			357.2.bl.a.10.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.17601 + 0.286477i) q^{2} +(-0.442289 + 0.896873i) q^{3} +(2.72109 + 0.729115i) q^{4} +(1.07834 + 0.945678i) q^{5} +(-1.21936 + 1.82490i) q^{6} +(0.241071 + 2.63475i) q^{7} +(1.65682 + 0.686276i) q^{8} +(-0.608761 - 0.793353i) q^{9} +(2.07556 + 2.36672i) q^{10} +(-4.77367 - 0.312883i) q^{11} +(-1.85743 + 2.11800i) q^{12} +(4.50138 - 4.50138i) q^{13} +(-0.230220 + 5.80229i) q^{14} +(-1.32509 + 0.548870i) q^{15} +(-1.47069 - 0.849103i) q^{16} +(4.08363 - 0.569174i) q^{17} +(-1.09739 - 1.90074i) q^{18} +(-0.367867 + 2.79423i) q^{19} +(2.24475 + 3.35951i) q^{20} +(-2.46965 - 0.949108i) q^{21} +(-10.2979 - 2.04838i) q^{22} +(1.14225 - 0.563294i) q^{23} +(-1.34829 + 1.18242i) q^{24} +(-0.384123 - 2.91770i) q^{25} +(11.0846 - 8.50551i) q^{26} +(0.980785 - 0.195090i) q^{27} +(-1.26505 + 7.34516i) q^{28} +(0.234713 - 1.17998i) q^{29} +(-3.04065 + 0.814738i) q^{30} +(1.66173 + 0.819477i) q^{31} +(-5.80246 - 4.45239i) q^{32} +(2.39196 - 4.14299i) q^{33} +(9.04907 - 0.0686616i) q^{34} +(-2.23166 + 3.06912i) q^{35} +(-1.07805 - 2.60265i) q^{36} +(0.312376 + 4.76594i) q^{37} +(-1.60097 + 5.97489i) q^{38} +(2.04626 + 6.02808i) q^{39} +(1.13761 + 2.30685i) q^{40} +(-2.29246 - 11.5250i) q^{41} +(-5.10209 - 2.77277i) q^{42} +(2.19051 - 5.28837i) q^{43} +(-12.7615 - 4.33194i) q^{44} +(0.0938055 - 1.43120i) q^{45} +(2.64691 - 0.898506i) q^{46} +(1.67824 + 6.26327i) q^{47} +(1.41201 - 0.943472i) q^{48} +(-6.88377 + 1.27032i) q^{49} -6.45899i q^{50} +(-1.29567 + 3.91424i) q^{51} +(15.5307 - 8.96666i) q^{52} +(-1.55650 + 2.02848i) q^{53} +(2.19009 - 0.143546i) q^{54} +(-4.85174 - 4.85174i) q^{55} +(-1.40875 + 4.53073i) q^{56} +(-2.34337 - 1.56579i) q^{57} +(0.848774 - 2.50041i) q^{58} +(-10.5929 + 1.39458i) q^{59} +(-4.00588 + 0.527384i) q^{60} +(-3.94372 + 11.6178i) q^{61} +(3.38119 + 2.25924i) q^{62} +(1.94353 - 1.79519i) q^{63} +(-8.94908 - 8.94908i) q^{64} +(9.11087 - 0.597158i) q^{65} +(6.39179 - 8.32994i) q^{66} +(6.44146 - 3.71898i) q^{67} +(11.5269 + 1.42866i) q^{68} +1.27359i q^{69} +(-5.73535 + 6.03912i) q^{70} +(-5.14800 + 3.43979i) q^{71} +(-0.464147 - 1.73222i) q^{72} +(1.15208 - 0.391078i) q^{73} +(-0.685599 + 10.4602i) q^{74} +(2.78670 + 0.945958i) q^{75} +(-3.03832 + 7.33515i) q^{76} +(-0.326429 - 12.6528i) q^{77} +(2.72577 + 13.7034i) q^{78} +(-7.56194 - 15.3341i) q^{79} +(-0.782923 - 2.30642i) q^{80} +(-0.258819 + 0.965926i) q^{81} +(-1.68677 - 25.7352i) q^{82} +(-2.46624 - 5.95403i) q^{83} +(-6.02815 - 4.38327i) q^{84} +(4.94179 + 3.24804i) q^{85} +(6.28158 - 10.8800i) q^{86} +(0.954481 + 0.732399i) q^{87} +(-7.69436 - 3.79444i) q^{88} +(-8.90368 + 2.38573i) q^{89} +(0.614126 - 3.08742i) q^{90} +(12.9452 + 10.7748i) q^{91} +(3.51887 - 0.699947i) q^{92} +(-1.46993 + 1.12792i) q^{93} +(1.85758 + 14.1097i) q^{94} +(-3.03913 + 2.66524i) q^{95} +(6.55959 - 3.23483i) q^{96} +(6.87580 + 1.36768i) q^{97} +(-15.3431 + 0.792195i) q^{98} +(2.65780 + 3.97768i) 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 $

$2$	2.17601	+	0.286477i	1.53867	+	0.202570i	0.851667	−	0.524084i	$-0.175592\pi$
$2$	2.17601	+	0.286477i	1.53867	+	0.202570i	0.687004	+	0.726654i	$0.258925\pi$
$3$	−0.442289	+	0.896873i	−0.255355	+	0.517810i
$3$	−0.442289	+	0.896873i	−0.255355	+	0.517810i
$4$	2.72109	+	0.729115i	1.36055	+	0.364558i
$5$	1.07834	+	0.945678i	0.482248	+	0.422920i	0.865641	−	0.500665i	$-0.166911\pi$
$5$	1.07834	+	0.945678i	0.482248	+	0.422920i	−0.383393	+	0.923585i	$0.625245\pi$
$6$	−1.21936	+	1.82490i	−0.497801	+	0.745011i
$7$	0.241071	+	2.63475i	0.0911164	+	0.995840i
$7$	0.241071	+	2.63475i	0.0911164	+	0.995840i
$8$	1.65682	+	0.686276i	0.585773	+	0.242635i
$9$	−0.608761	−	0.793353i	−0.202920	−	0.264451i
$10$	2.07556	+	2.36672i	0.656350	+	0.748423i
$11$	−4.77367	−	0.312883i	−1.43932	−	0.0943377i	−0.674351	−	0.738411i	$-0.735577\pi$
$11$	−4.77367	−	0.312883i	−1.43932	−	0.0943377i	−0.764964	+	0.644073i	$0.777243\pi$
$12$	−1.85743	+	2.11800i	−0.536195	+	0.611413i
$13$	4.50138	−	4.50138i	1.24846	−	1.24846i	0.292059	−	0.956400i	$-0.405660\pi$
$13$	4.50138	−	4.50138i	1.24846	−	1.24846i	0.956400	−	0.292059i	$-0.0943403\pi$
$14$	−0.230220	+	5.80229i	−0.0615290	+	1.55073i
$15$	−1.32509	+	0.548870i	−0.342137	+	0.141718i
$16$	−1.47069	−	0.849103i	−0.367672	−	0.212276i
$17$	4.08363	−	0.569174i	0.990426	−	0.138045i
$17$	4.08363	−	0.569174i	0.990426	−	0.138045i
$18$	−1.09739	−	1.90074i	−0.258658	−	0.448009i
$19$	−0.367867	+	2.79423i	−0.0843946	+	0.641041i	0.896008	+	0.444037i	$0.146454\pi$
$19$	−0.367867	+	2.79423i	−0.0843946	+	0.641041i	−0.980403	+	0.197003i	$0.936879\pi$
$20$	2.24475	+	3.35951i	0.501942	+	0.751209i
$21$	−2.46965	−	0.949108i	−0.538923	−	0.207112i
$22$	−10.2979	−	2.04838i	−2.19552	−	0.436716i
$23$	1.14225	−	0.563294i	0.238175	−	0.117455i	−0.319285	−	0.947659i	$-0.603443\pi$
$23$	1.14225	−	0.563294i	0.238175	−	0.117455i	0.557460	+	0.830204i	$0.311776\pi$
$24$	−1.34829	+	1.18242i	−0.275219	+	0.241361i
$25$	−0.384123	−	2.91770i	−0.0768246	−	0.583541i
$26$	11.0846	−	8.50551i	2.17387	−	1.66807i
$27$	0.980785	−	0.195090i	0.188752	−	0.0375451i
$28$	−1.26505	+	7.34516i	−0.239073	+	1.38810i
$29$	0.234713	−	1.17998i	0.0435850	−	0.219117i	−0.952854	−	0.303428i	$-0.901869\pi$
$29$	0.234713	−	1.17998i	0.0435850	−	0.219117i	0.996439	+	0.0843109i	$0.0268689\pi$
$30$	−3.04065	+	0.814738i	−0.555143	+	0.148750i
$31$	1.66173	+	0.819477i	0.298456	+	0.147182i	0.585352	−	0.810780i	$-0.300956\pi$
$31$	1.66173	+	0.819477i	0.298456	+	0.147182i	−0.286895	+	0.957962i	$0.592623\pi$
$32$	−5.80246	−	4.45239i	−1.02574	−	0.787078i
$33$	2.39196	−	4.14299i	0.416386	−	0.721202i
$34$	9.04907	−	0.0686616i	1.55190	−	0.0117754i
$35$	−2.23166	+	3.06912i	−0.377220	+	0.518777i
$36$	−1.07805	−	2.60265i	−0.179675	−	0.433774i
$37$	0.312376	+	4.76594i	0.0513543	+	0.783515i	0.943418	+	0.331606i	$0.107590\pi$
$37$	0.312376	+	4.76594i	0.0513543	+	0.783515i	−0.892064	+	0.451910i	$0.850743\pi$
$38$	−1.60097	+	5.97489i	−0.259711	+	0.969255i
$39$	2.04626	+	6.02808i	0.327663	+	0.965265i
$40$	1.13761	+	2.30685i	0.179872	+	0.364745i
$41$	−2.29246	−	11.5250i	−0.358022	−	1.79990i	−0.568925	−	0.822390i	$-0.692640\pi$
$41$	−2.29246	−	11.5250i	−0.358022	−	1.79990i	0.210903	−	0.977507i	$-0.432360\pi$
$42$	−5.10209	−	2.77277i	−0.787270	−	0.427847i
$43$	2.19051	−	5.28837i	0.334050	−	0.806469i	−0.664212	−	0.747544i	$-0.731233\pi$
$43$	2.19051	−	5.28837i	0.334050	−	0.806469i	0.998262	−	0.0589247i	$-0.0187672\pi$
$44$	−12.7615	−	4.33194i	−1.92386	−	0.653064i
$45$	0.0938055	−	1.43120i	0.0139837	−	0.213350i
$46$	2.64691	−	0.898506i	0.390266	−	0.132477i
$47$	1.67824	+	6.26327i	0.244796	+	0.913592i	0.973486	+	0.228748i	$0.0734631\pi$
$47$	1.67824	+	6.26327i	0.244796	+	0.913592i	−0.728689	+	0.684844i	$0.759870\pi$
$48$	1.41201	−	0.943472i	0.203806	−	0.136179i
$49$	−6.88377	+	1.27032i	−0.983396	+	0.181475i
$50$		−	6.45899i		−	0.913439i
$51$	−1.29567	+	3.91424i	−0.181430	+	0.548103i
$52$	15.5307	−	8.96666i	2.15372	−	1.24345i
$53$	−1.55650	+	2.02848i	−0.213802	+	0.278633i	−0.887926	−	0.459985i	$-0.847855\pi$
$53$	−1.55650	+	2.02848i	−0.213802	+	0.278633i	0.674124	+	0.738618i	$0.264521\pi$
$54$	2.19009	−	0.143546i	0.298033	−	0.0195341i
$55$	−4.85174	−	4.85174i	−0.654209	−	0.654209i
$56$	−1.40875	+	4.53073i	−0.188252	+	0.605444i
$57$	−2.34337	−	1.56579i	−0.310386	−	0.207394i
$58$	0.848774	−	2.50041i	0.111449	−	0.328320i
$59$	−10.5929	+	1.39458i	−1.37908	+	0.181559i	−0.783327	−	0.621610i	$-0.786479\pi$
$59$	−10.5929	+	1.39458i	−1.37908	+	0.181559i	−0.595751	+	0.803169i	$0.703145\pi$
$60$	−4.00588	+	0.527384i	−0.517157	+	0.0680850i
$61$	−3.94372	+	11.6178i	−0.504942	+	1.48751i	0.333621	+	0.942707i	$0.391729\pi$
$61$	−3.94372	+	11.6178i	−0.504942	+	1.48751i	−0.838563	+	0.544804i	$0.816604\pi$
$62$	3.38119	+	2.25924i	0.429411	+	0.286923i
$63$	1.94353	−	1.79519i	0.244862	−	0.226172i
$64$	−8.94908	−	8.94908i	−1.11864	−	1.11864i
$65$	9.11087	−	0.597158i	1.13006	−	0.0740684i
$66$	6.39179	−	8.32994i	0.786775	−	1.02534i
$67$	6.44146	−	3.71898i	0.786949	−	0.454345i	−0.0519381	−	0.998650i	$-0.516540\pi$
$67$	6.44146	−	3.71898i	0.786949	−	0.454345i	0.838887	+	0.544305i	$0.183207\pi$
$68$	11.5269	+	1.42866i	1.39785	+	0.173250i
$69$			1.27359i			0.153322i
$70$	−5.73535	+	6.03912i	−0.685506	+	0.721813i
$71$	−5.14800	+	3.43979i	−0.610956	+	0.408227i	−0.822194	−	0.569207i	$-0.807250\pi$
$71$	−5.14800	+	3.43979i	−0.610956	+	0.408227i	0.211239	+	0.977435i	$0.432250\pi$
$72$	−0.464147	−	1.73222i	−0.0547002	−	0.204144i
$73$	1.15208	−	0.391078i	0.134840	−	0.0457722i	−0.253203	−	0.967413i	$-0.581484\pi$
$73$	1.15208	−	0.391078i	0.134840	−	0.0457722i	0.388044	+	0.921641i	$0.373151\pi$
$74$	−0.685599	+	10.4602i	−0.0796992	+	1.21597i
$75$	2.78670	+	0.945958i	0.321781	+	0.109230i
$76$	−3.03832	+	7.33515i	−0.348519	+	0.841399i
$77$	−0.326429	−	12.6528i	−0.0372000	−	1.44192i
$78$	2.72577	+	13.7034i	0.308632	+	1.55160i
$79$	−7.56194	−	15.3341i	−0.850784	−	1.72522i	−0.670921	−	0.741529i	$-0.734101\pi$
$79$	−7.56194	−	15.3341i	−0.850784	−	1.72522i	−0.179863	−	0.983692i	$-0.557566\pi$
$80$	−0.782923	−	2.30642i	−0.0875335	−	0.257865i
$81$	−0.258819	+	0.965926i	−0.0287577	+	0.107325i
$82$	−1.68677	−	25.7352i	−0.186273	−	2.84197i
$83$	−2.46624	−	5.95403i	−0.270705	−	0.653540i	0.728809	−	0.684717i	$-0.240074\pi$
$83$	−2.46624	−	5.95403i	−0.270705	−	0.653540i	−0.999514	+	0.0311775i	$0.990074\pi$
$84$	−6.02815	−	4.38327i	−0.657726	−	0.478254i
$85$	4.94179	+	3.24804i	0.536013	+	0.352299i
$86$	6.28158	−	10.8800i	0.677360	−	1.17322i
$87$	0.954481	+	0.732399i	0.102331	+	0.0785214i
$88$	−7.69436	−	3.79444i	−0.820222	−	0.404489i
$89$	−8.90368	+	2.38573i	−0.943788	+	0.252887i	−0.697724	−	0.716366i	$-0.745804\pi$
$89$	−8.90368	+	2.38573i	−0.943788	+	0.252887i	−0.246064	+	0.969254i	$0.579137\pi$
$90$	0.614126	−	3.08742i	0.0647346	−	0.325443i
$91$	12.9452	+	10.7748i	1.35702	+	1.12951i
$92$	3.51887	−	0.699947i	0.366868	−	0.0729745i
$93$	−1.46993	+	1.12792i	−0.152425	+	0.116960i
$94$	1.85758	+	14.1097i	0.191595	+	1.45531i
$95$	−3.03913	+	2.66524i	−0.311808	+	0.273448i
$96$	6.55959	−	3.23483i	0.669485	−	0.330154i
$97$	6.87580	+	1.36768i	0.698132	+	0.138867i	0.531382	−	0.847132i	$-0.321673\pi$
$97$	6.87580	+	1.36768i	0.698132	+	0.138867i	0.166750	+	0.985999i	$0.446673\pi$
$98$	−15.3431	+	0.792195i	−1.54988	+	0.0800237i
$99$	2.65780	+	3.97768i	0.267119	+	0.399772i
$100$	1.08211	−	8.21941i	0.108211	−	0.821941i
$101$	2.87274	+	4.97573i	0.285848	+	0.495104i	0.972815	−	0.231585i	$-0.0743913\pi$
$101$	2.87274	+	4.97573i	0.285848	+	0.495104i	−0.686966	+	0.726689i	$0.741058\pi$
$102$	−3.94072	+	8.14623i	−0.390190	+	0.806597i
$103$	7.94638	+	4.58784i	0.782980	+	0.452054i	0.837485	−	0.546460i	$-0.184025\pi$
$103$	7.94638	+	4.58784i	0.782980	+	0.452054i	−0.0545056	+	0.998513i	$0.517358\pi$
$104$	10.5472	−	4.36877i	1.03423	−	0.428393i
$105$	−1.76557	−	3.35896i	−0.172302	−	0.327801i
$106$	−3.96808	+	3.96808i	−0.385414	+	0.385414i
$107$	−4.73477	+	5.39898i	−0.457728	+	0.521939i	−0.933958	−	0.357382i	$-0.883669\pi$
$107$	−4.73477	+	5.39898i	−0.457728	+	0.521939i	0.476230	+	0.879321i	$0.342003\pi$
$108$	2.81105	+	0.184246i	0.270494	+	0.0177291i
$109$	10.8840	+	12.4109i	1.04250	+	1.18874i	0.981669	+	0.190596i	$0.0610421\pi$
$109$	10.8840	+	12.4109i	1.04250	+	1.18874i	0.0608321	+	0.998148i	$0.480625\pi$
$110$	−9.16753	−	11.9474i	−0.874089	−	1.13914i
$111$	−4.41260	−	1.82776i	−0.418825	−	0.173483i
$112$	1.88263	−	4.07959i	0.177892	−	0.385485i
$113$	−9.51296	+	14.2371i	−0.894904	+	1.33932i	0.0453954	+	0.998969i	$0.485545\pi$
$113$	−9.51296	+	14.2371i	−0.894904	+	1.33932i	−0.940299	+	0.340349i	$0.889455\pi$
$114$	−4.65062	−	4.07849i	−0.435571	−	0.381985i
$115$	1.76443	+	0.472776i	0.164534	+	0.0440866i
$116$	1.49902	−	3.03970i	0.139180	−	0.282229i
$117$	−6.31146	−	0.830919i	−0.583494	−	0.0768185i
$118$	−23.4497			−2.15872
$119$	2.48408	+	10.6221i	0.227715	+	0.973728i
$120$	−2.57211			−0.234800
$121$	11.7841	+	1.55141i	1.07128	+	0.141037i
$122$	−11.9098	+	24.1507i	−1.07826	+	2.18650i
$123$	11.3504	+	3.04132i	1.02343	+	0.274226i
$124$	3.92424	+	3.44147i	0.352407	+	0.309053i
$125$	6.32917	−	9.47227i	0.566098	−	0.847226i
$126$	4.74342	−	3.34957i	0.422577	−	0.298403i
$127$	6.67577	+	2.76520i	0.592379	+	0.245371i	0.658674	−	0.752429i	$-0.271118\pi$
$127$	6.67577	+	2.76520i	0.592379	+	0.245371i	−0.0662948	+	0.997800i	$0.521118\pi$
$128$	−8.00480	−	10.4321i	−0.707531	−	0.922073i
$129$	3.77416	+	4.30360i	0.332296	+	0.378911i
$130$	19.9964	+	1.31063i	1.75380	+	0.114950i
$131$	6.44099	−	7.34454i	0.562752	−	0.641695i	−0.398565	−	0.917140i	$-0.630492\pi$
$131$	6.44099	−	7.34454i	0.562752	−	0.641695i	0.961317	+	0.275445i	$0.0888251\pi$
$132$	9.52945	−	9.52945i	0.829432	−	0.829432i
$133$	−7.45077	−	0.295628i	−0.646064	−	0.0256342i
$134$	15.0821	−	6.24720i	1.30289	−	0.539676i
$135$	1.24211	+	0.717133i	0.106904	+	0.0617210i
$136$	7.15643	+	1.85948i	0.613659	+	0.159449i
$137$	1.51625	+	2.62622i	0.129542	+	0.224373i	0.923499	−	0.383601i	$-0.125316\pi$
$137$	1.51625	+	2.62622i	0.129542	+	0.224373i	−0.793957	+	0.607973i	$0.791983\pi$
$138$	−0.364854	+	2.77134i	−0.0310585	+	0.235912i
$139$	10.5174	+	15.7404i	0.892072	+	1.33508i	0.941749	+	0.336315i	$0.109181\pi$
$139$	10.5174	+	15.7404i	0.892072	+	1.33508i	−0.0496770	+	0.998765i	$0.515819\pi$
$140$	−8.31031	+	6.72424i	−0.702349	+	0.568302i
$141$	−6.35962	−	1.26501i	−0.535577	−	0.106533i
$142$	−12.1875	+	6.01022i	−1.02275	+	0.504366i
$143$	−22.8965	+	20.0797i	−1.91470	+	1.67915i
$144$	0.221660	+	1.68368i	0.0184717	+	0.140306i
$145$	1.36898	−	1.05046i	0.113688	−	0.0872356i
$146$	2.61897	−	0.520945i	0.216747	−	0.0431137i
$147$	1.90529	−	6.73571i	0.157146	−	0.555552i
$148$	−2.62491	+	13.1963i	−0.215766	+	1.08473i
$149$	−18.4789	+	4.95139i	−1.51385	+	0.405634i	−0.917711	−	0.397249i	$-0.869965\pi$
$149$	−18.4789	+	4.95139i	−1.51385	+	0.405634i	−0.596136	+	0.802883i	$0.703298\pi$
$150$	5.79289	+	2.85674i	0.472988	+	0.233252i
$151$	7.38052	+	5.66327i	0.600618	+	0.460870i	0.863772	−	0.503884i	$-0.168096\pi$
$151$	7.38052	+	5.66327i	0.600618	+	0.460870i	−0.263154	+	0.964754i	$0.584763\pi$
$152$	−2.52710	+	4.37707i	−0.204975	+	0.355027i
$153$	−2.93751	−	2.89327i	−0.237484	−	0.233907i
$154$	2.91443	−	27.6262i	0.234852	−	2.22618i
$155$	1.01695	+	2.45514i	0.0816835	+	0.197201i
$156$	1.17290	+	17.8949i	0.0939068	+	1.43274i
$157$	−0.418117	+	1.56043i	−0.0333693	+	0.124536i	−0.980601	−	0.196013i	$-0.937201\pi$
$157$	−0.418117	+	1.56043i	−0.0333693	+	0.124536i	0.947232	+	0.320549i	$0.103867\pi$
$158$	−12.0620	−	35.5334i	−0.959600	−	2.82689i
$159$	−1.13086	−	2.29316i	−0.0896831	−	0.181859i
$160$	−2.04650	−	10.2884i	−0.161790	−	0.813373i
$161$	1.75950	+	2.87374i	0.138668	+	0.226482i
$162$	−0.839908	+	2.02772i	−0.0659894	+	0.159313i
$163$	−11.6567	−	3.95692i	−0.913025	−	0.309930i	−0.174894	−	0.984587i	$-0.555958\pi$
$163$	−11.6567	−	3.95692i	−0.913025	−	0.309930i	−0.738131	+	0.674657i	$0.764291\pi$
$164$	2.16503	−	33.0320i	0.169060	−	2.57936i
$165$	6.49727	−	2.20553i	0.505812	−	0.171700i
$166$	−3.66087	−	13.6625i	−0.284138	−	1.06042i
$167$	0.780435	−	0.521470i	0.0603918	−	0.0403525i	−0.525008	−	0.851097i	$-0.675938\pi$
$167$	0.780435	−	0.521470i	0.0603918	−	0.0403525i	0.585400	+	0.810745i	$0.300938\pi$
$168$	−3.44041	−	3.26736i	−0.265434	−	0.252082i
$169$		−	27.5249i		−	2.11730i
$170$	9.82290	+	8.48347i	0.753382	+	0.650652i
$171$	2.44076	−	1.40917i	0.186649	−	0.107762i
$172$	9.81643	−	12.7930i	0.748496	−	0.975458i
$173$	−2.67180	+	0.175119i	−0.203133	+	0.0133141i	−0.166630	−	0.986019i	$-0.553289\pi$
$173$	−2.67180	+	0.175119i	−0.203133	+	0.0133141i	−0.0365032	+	0.999334i	$0.511622\pi$
$174$	1.86714	+	1.86714i	0.141548	+	0.141548i
$175$	7.59480	−	1.71544i	0.574113	−	0.129675i
$176$	6.75491	+	4.51349i	0.509171	+	0.340217i
$177$	3.43436	−	10.1173i	0.258142	−	0.760462i
$178$	−20.0579	+	2.64068i	−1.50341	+	0.197927i
$179$	−2.87318	+	0.378261i	−0.214751	+	0.0282726i	−0.237134	−	0.971477i	$-0.576208\pi$
$179$	−2.87318	+	0.378261i	−0.214751	+	0.0282726i	0.0223827	+	0.999749i	$0.492875\pi$
$180$	1.29876	−	3.82602i	0.0968038	−	0.285175i
$181$	1.32089	+	0.882593i	0.0981812	+	0.0656026i	0.603692	−	0.797218i	$-0.293696\pi$
$181$	1.32089	+	0.882593i	0.0981812	+	0.0656026i	−0.505510	+	0.862820i	$0.668696\pi$
$182$	25.0820	+	27.1546i	1.85920	+	2.01284i
$183$	−8.67545	−	8.67545i	−0.641308	−	0.641308i
$184$	2.27907	−	0.149378i	0.168015	−	0.0110123i
$185$	−4.17019	+	5.43470i	−0.306599	+	0.399567i
$186$	−3.52171	+	2.03326i	−0.258224	+	0.149086i
$187$	−19.6720	+	1.43935i	−1.43856	+	0.105256i
$188$			18.2666i			1.33223i
$189$	0.750453	+	2.53709i	0.0545874	+	0.184546i
$190$	−7.37670	+	4.92895i	−0.535162	+	0.357584i
$191$	−3.84211	−	14.3389i	−0.278005	−	1.03753i	−0.953801	−	0.300440i	$-0.902866\pi$
$191$	−3.84211	−	14.3389i	−0.278005	−	1.03753i	0.675795	−	0.737089i	$-0.263800\pi$
$192$	11.9843	−	4.06811i	0.864890	−	0.293591i
$193$	0.224275	−	3.42177i	0.0161436	−	0.246304i	−0.982158	−	0.188055i	$-0.939782\pi$
$193$	0.224275	−	3.42177i	0.0161436	−	0.246304i	0.998302	−	0.0582490i	$-0.0185517\pi$
$194$	14.5700	+	4.94585i	1.04606	+	0.355091i
$195$	−3.49406	+	8.43541i	−0.250215	+	0.604072i
$196$	−19.6576	−	1.56239i	−1.40411	−	0.111599i
$197$	−0.419694	−	2.10994i	−0.0299019	−	0.150327i	0.962950	−	0.269680i	$-0.0869180\pi$
$197$	−0.419694	−	2.10994i	−0.0299019	−	0.150327i	−0.992852	+	0.119353i	$0.961918\pi$
$198$	4.64388	+	9.41686i	0.330026	+	0.669227i
$199$	5.77301	+	17.0067i	0.409238	+	1.20558i	0.934909	+	0.354888i	$0.115481\pi$
$199$	5.77301	+	17.0067i	0.409238	+	1.20558i	−0.525671	+	0.850688i	$0.676186\pi$
$200$	1.36593	−	5.09771i	0.0965856	−	0.360463i
$201$	0.486466	+	7.42203i	0.0343126	+	0.523510i
$202$	4.82568	+	11.6502i	0.339533	+	0.819706i
$203$	3.16553	+	0.333949i	0.222177	+	0.0234386i
$204$	−6.37956	+	9.70632i	−0.446659	+	0.679578i
$205$	8.42685	−	14.5957i	0.588557	−	1.01941i
$206$	15.9771	+	12.2596i	1.11318	+	0.854170i
$207$	−1.14225	−	0.563294i	−0.0793917	−	0.0391517i
$208$	−10.4423	+	2.79800i	−0.724041	+	0.194006i
$209$	2.63034	−	13.2236i	0.181945	−	0.914698i
$210$	−2.87964	−	7.81492i	−0.198714	−	0.539280i
$211$	−13.5077	+	2.68685i	−0.929908	+	0.184970i	−0.636729	−	0.771087i	$-0.719713\pi$
$211$	−13.5077	+	2.68685i	−0.929908	+	0.184970i	−0.293179	+	0.956058i	$0.594713\pi$
$212$	−5.71439	+	4.38481i	−0.392466	+	0.301150i
$213$	−0.808147	−	6.13848i	−0.0553733	−	0.420602i
$214$	−11.8496	+	10.3918i	−0.810022	+	0.710370i
$215$	7.36321	−	3.63113i	0.502167	−	0.247641i
$216$	1.75887	+	0.349860i	0.119676	+	0.0238050i
$217$	−1.75852	+	4.57580i	−0.119376	+	0.310626i
$218$	20.1283	+	30.1242i	1.36326	+	2.04026i
$219$	−0.158804	+	1.20624i	−0.0107310	+	0.0815099i
$220$	−9.66457	−	16.7395i	−0.651585	−	1.12858i
$221$	15.8199	−	20.9441i	1.06416	−	1.40885i
$222$	−9.07825	−	5.24133i	−0.609292	−	0.351775i
$223$	−7.91340	+	3.27784i	−0.529920	+	0.219500i	−0.631568	−	0.775320i	$-0.717588\pi$
$223$	−7.91340	+	3.27784i	−0.529920	+	0.219500i	0.101648	+	0.994820i	$0.467588\pi$
$224$	10.3321	−	16.3614i	0.690342	−	1.09319i
$225$	−2.08093	+	2.08093i	−0.138729	+	0.138729i
$226$	−24.7789	+	28.2549i	−1.64827	+	1.87949i
$227$	8.68868	+	0.569486i	0.576688	+	0.0377981i	0.350957	−	0.936392i	$-0.385856\pi$
$227$	8.68868	+	0.569486i	0.576688	+	0.0377981i	0.225731	+	0.974190i	$0.427523\pi$
$228$	−5.23488	−	5.96924i	−0.346688	−	0.395322i
$229$	9.09230	+	11.8493i	0.600836	+	0.783025i	0.990438	−	0.137959i	$-0.0440541\pi$
$229$	9.09230	+	11.8493i	0.600836	+	0.783025i	−0.389602	+	0.920983i	$0.627387\pi$
$230$	3.70397	+	1.53423i	0.244232	+	0.101164i
$231$	11.4924	+	5.30344i	0.756141	+	0.348941i
$232$	1.19867	−	1.79393i	0.0786964	−	0.117777i
$233$	−15.3324	−	13.4462i	−1.00446	−	0.880888i	−0.0115718	−	0.999933i	$-0.503684\pi$
$233$	−15.3324	−	13.4462i	−1.00446	−	0.880888i	−0.992889	+	0.119045i	$0.962017\pi$
$234$	−13.4957	−	3.61617i	−0.882245	−	0.236397i
$235$	−4.11333	+	8.34100i	−0.268324	+	0.544107i
$236$	−29.8411	−	3.92865i	−1.94249	−	0.255733i
$237$	17.0973			1.11059
$238$	2.36238	+	23.8255i	0.153130	+	1.54437i
$239$	15.4216			0.997543			0.498772	−	0.866733i	$-0.333785\pi$
$239$	15.4216			0.997543			0.498772	+	0.866733i	$0.333785\pi$
$240$	2.41484	+	0.317920i	0.155877	+	0.0205216i
$241$	6.42935	−	13.0374i	0.414151	−	0.839815i	−0.585426	−	0.810726i	$-0.699073\pi$
$241$	6.42935	−	13.0374i	0.414151	−	0.839815i	0.999577	−	0.0290891i	$-0.00926065\pi$
$242$	25.1979	+	6.75176i	1.61978	+	0.434019i
$243$	−0.751840	−	0.659346i	−0.0482305	−	0.0422971i
$244$	−19.2020	+	28.7378i	−1.22928	+	1.83975i
$245$	−8.62435	−	5.13999i	−0.550990	−	0.328382i
$246$	23.8272	+	9.86955i	1.51917	+	0.629259i
$247$	10.9220	+	14.2338i	0.694950	+	0.905676i
$248$	2.19080	+	2.49813i	0.139116	+	0.158631i
$249$	6.43080	+	0.421497i	0.407535	+	0.0267113i
$250$	16.4859	−	18.7986i	1.04266	−	1.18893i
$251$	−3.63027	+	3.63027i	−0.229140	+	0.229140i	−0.812334	−	0.583193i	$-0.801803\pi$
$251$	−3.63027	+	3.63027i	−0.229140	+	0.229140i	0.583193	+	0.812334i	$0.301803\pi$
$252$	6.59742	−	3.46781i	0.415599	−	0.218452i
$253$	−5.62896	+	2.33159i	−0.353890	+	0.146586i
$254$	13.7344	+	7.92955i	0.861771	+	0.497544i
$255$	−5.09877	+	2.99559i	−0.319298	+	0.187591i
$256$	−1.77406	−	3.07276i	−0.110879	−	0.192048i
$257$	1.49236	−	11.3356i	0.0930907	−	0.707094i	−0.879720	−	0.475492i	$-0.842270\pi$
$257$	1.49236	−	11.3356i	0.0930907	−	0.707094i	0.972811	−	0.231602i	$-0.0743966\pi$
$258$	6.97971	+	10.4459i	0.434538	+	0.650332i
$259$	−12.4817	+	1.97196i	−0.775577	+	0.122532i
$260$	25.2269	+	5.01795i	1.56451	+	0.311200i
$261$	−1.07903	+	0.532116i	−0.0667900	+	0.0329372i
$262$	16.1197	−	14.1366i	0.995878	−	0.873361i
$263$	1.82066	+	13.8293i	0.112267	+	0.852751i	0.951213	+	0.308536i	$0.0998390\pi$
$263$	1.82066	+	13.8293i	0.112267	+	0.852751i	−0.838946	+	0.544215i	$0.816828\pi$
$264$	6.80626	−	5.22263i	0.418896	−	0.321430i
$265$	−3.59672	+	0.715433i	−0.220945	+	0.0439487i
$266$	−16.1283	−	2.77776i	−0.988887	−	0.170316i
$267$	1.79830	−	9.04065i	0.110054	−	0.553279i
$268$	20.2394	−	5.42312i	1.23632	−	0.331270i
$269$	−2.25844	−	1.11374i	−0.137699	−	0.0679058i	0.372134	−	0.928179i	$-0.378626\pi$
$269$	−2.25844	−	1.11374i	−0.137699	−	0.0679058i	−0.509833	+	0.860273i	$0.670293\pi$
$270$	2.49740	+	1.91632i	0.151987	+	0.116624i
$271$	5.34684	−	9.26099i	0.324797	−	0.562565i	−0.656674	−	0.754175i	$-0.728037\pi$
$271$	5.34684	−	9.26099i	0.324797	−	0.562565i	0.981471	+	0.191609i	$0.0613706\pi$
$272$	−6.48904	−	2.63034i	−0.393456	−	0.159488i
$273$	−15.3892	+	6.84456i	−0.931394	+	0.414252i
$274$	2.54702	+	6.14904i	0.153871	+	0.371477i
$275$	0.920776	+	14.0483i	0.0555249	+	0.847146i
$276$	−0.928594	+	3.46556i	−0.0558948	+	0.208602i
$277$	−4.22322	−	12.4412i	−0.253749	−	0.747520i	−0.996920	−	0.0784193i	$-0.975013\pi$
$277$	−4.22322	−	12.4412i	−0.253749	−	0.747520i	0.743172	−	0.669101i	$-0.233321\pi$
$278$	18.3767	+	37.2642i	1.10216	+	2.23496i
$279$	−0.361465	−	1.81721i	−0.0216404	−	0.108793i
$280$	−5.80372	+	3.55344i	−0.346839	+	0.212358i
$281$	10.9568	−	26.4522i	0.653630	−	1.57800i	−0.153841	−	0.988096i	$-0.549164\pi$
$281$	10.9568	−	26.4522i	0.653630	−	1.57800i	0.807471	−	0.589907i	$-0.200836\pi$
$282$	−13.4762	−	4.57455i	−0.802496	−	0.272411i
$283$	−0.266950	+	4.07287i	−0.0158685	+	0.242107i	0.982555	+	0.185974i	$0.0595439\pi$
$283$	−0.266950	+	4.07287i	−0.0158685	+	0.242107i	−0.998423	+	0.0561334i	$0.982123\pi$
$284$	−16.5162	+	5.60649i	−0.980056	+	0.332684i
$285$	−1.04621	−	3.90452i	−0.0619723	−	0.231284i
$286$	−55.5754	+	37.1343i	−3.28624	+	2.19580i
$287$	29.8127	−	8.81838i	1.75979	−	0.520533i
$288$			7.31385i			0.430973i
$289$	16.3521	−	4.64859i	0.961887	−	0.273447i
$290$	3.27985	−	1.89362i	0.192599	−	0.111197i
$291$	−4.26772	+	5.56181i	−0.250178	+	0.326039i
$292$	3.42005	−	0.224162i	0.200143	−	0.0131181i
$293$	10.9507	+	10.9507i	0.639746	+	0.639746i	0.950493	−	0.310747i	$-0.100579\pi$
$293$	10.9507	+	10.9507i	0.639746	+	0.639746i	−0.310747	+	0.950493i	$0.600579\pi$
$294$	6.07557	−	14.1112i	0.354334	−	0.822979i
$295$	−12.7416	−	8.51363i	−0.741842	−	0.495683i
$296$	−2.75320	+	8.11066i	−0.160026	+	0.471422i
$297$	−4.74298	+	0.624426i	−0.275216	+	0.0362329i
$298$	−41.6286	+	5.48051i	−2.41148	+	0.317477i
$299$	2.60609	−	7.67730i	0.150714	−	0.443990i
$300$	6.89316	+	4.60587i	0.397977	+	0.265920i
$301$	14.4616	+	4.49657i	0.833552	+	0.259178i
$302$	14.4377	+	14.4377i	0.830795	+	0.830795i
$303$	−5.73318	+	0.375772i	−0.329363	+	0.0215876i
$304$	2.91361	−	3.79709i	0.167107	−	0.217778i
$305$	−15.2394	+	8.79847i	−0.872605	+	0.503799i
$306$	−5.56320	−	7.13731i	−0.318027	−	0.408013i
$307$		−	21.4072i		−	1.22178i	−0.791717	−	0.610888i	$-0.790813\pi$
$307$		−	21.4072i		−	1.22178i	0.791717	−	0.610888i	$-0.209187\pi$
$308$	8.33712	−	34.6675i	0.475052	−	1.97537i
$309$	−7.62930	+	5.09774i	−0.434016	+	0.290000i
$310$	1.50956	+	5.63374i	0.0857370	+	0.319975i
$311$	−8.46610	+	2.87386i	−0.480069	+	0.162961i	−0.550975	−	0.834522i	$-0.685744\pi$
$311$	−8.46610	+	2.87386i	−0.480069	+	0.162961i	0.0709065	+	0.997483i	$0.477411\pi$
$312$	−0.746652	+	11.3917i	−0.0422709	+	0.644929i
$313$	−12.1533	−	4.12549i	−0.686946	−	0.233187i	−0.0439244	−	0.999035i	$-0.513986\pi$
$313$	−12.1533	−	4.12549i	−0.686946	−	0.233187i	−0.643021	+	0.765848i	$0.722319\pi$
$314$	−1.35685	+	3.27573i	−0.0765717	+	0.184860i
$315$	3.79345	−	0.0978667i	0.213737	−	0.00551417i
$316$	−9.39643	−	47.2390i	−0.528590	−	2.65740i
$317$	4.53992	+	9.20605i	0.254987	+	0.517063i	0.986296	−	0.164983i	$-0.0527569\pi$
$317$	4.53992	+	9.20605i	0.254987	+	0.517063i	−0.731309	+	0.682046i	$0.761090\pi$
$318$	−1.80383	−	5.31390i	−0.101154	−	0.297989i
$319$	−1.48964	+	5.55940i	−0.0834036	+	0.311266i
$320$	−1.18719	−	18.1131i	−0.0663662	−	1.01255i
$321$	−2.74806	−	6.63440i	−0.153382	−	0.370296i
$322$	3.00543	+	6.75734i	0.167486	+	0.376572i
$323$	0.0881690	+	11.6200i	0.00490585	+	0.646553i
$324$	−1.40854	+	2.43967i	−0.0782523	+	0.135537i
$325$	−14.8628	−	11.4046i	−0.824439	−	0.632614i
$326$	−24.2316	−	11.9497i	−1.34206	−	0.661832i
$327$	−15.9448	+	4.27241i	−0.881752	+	0.236265i
$328$	4.11112	−	20.6680i	0.226999	−	1.14120i
$329$	−16.0976	+	5.93163i	−0.887487	+	0.327021i
$330$	14.7699	−	2.93793i	0.813059	−	0.161727i
$331$	11.2077	−	8.59993i	0.616028	−	0.472695i	−0.252994	−	0.967468i	$-0.581415\pi$
$331$	11.2077	−	8.59993i	0.616028	−	0.472695i	0.869022	+	0.494773i	$0.164749\pi$
$332$	−2.36970	−	17.9997i	−0.130054	−	0.987859i
$333$	3.59091	−	3.14914i	0.196781	−	0.172572i
$334$	1.84762	−	0.911146i	0.101097	−	0.0498557i
$335$	10.4630	+	2.08123i	0.571656	+	0.113709i
$336$	2.82620	+	3.49283i	0.154182	+	0.190550i
$337$	2.45834	+	3.67917i	0.133914	+	0.200417i	0.892366	−	0.451312i	$-0.149044\pi$
$337$	2.45834	+	3.67917i	0.133914	+	0.200417i	−0.758452	+	0.651729i	$0.774044\pi$
$338$	7.88525	−	59.8944i	0.428901	−	3.25783i
$339$	−8.56144	−	14.8288i	−0.464993	−	0.805392i
$340$	11.0789	+	12.4413i	0.600837	+	0.674727i
$341$	−7.67617	−	4.43184i	−0.415688	−	0.239997i
$342$	5.71480	−	2.36715i	0.309021	−	0.128001i
$343$	−5.00646	−	17.8307i	−0.270323	−	0.962770i
$344$	7.25856	−	7.25856i	0.391355	−	0.391355i
$345$	−1.20441	+	1.37336i	−0.0648430	+	0.0739393i
$346$	−5.86403	−	0.384349i	−0.315252	−	0.0206627i
$347$	−19.2653	−	21.9679i	−1.03422	−	1.17930i	−0.983560	−	0.180580i	$-0.942202\pi$
$347$	−19.2653	−	21.9679i	−1.03422	−	1.17930i	−0.0506550	−	0.998716i	$-0.516131\pi$
$348$	2.06323	+	2.68885i	0.110601	+	0.144138i
$349$	−10.7689	−	4.46060i	−0.576443	−	0.238771i	0.0753629	−	0.997156i	$-0.475988\pi$
$349$	−10.7689	−	4.46060i	−0.576443	−	0.238771i	−0.651806	+	0.758386i	$0.725988\pi$
$350$	17.0178	−	1.55708i	0.909639	−	0.0832293i
$351$	3.53671	−	5.29307i	0.188776	−	0.282523i
$352$	26.3060	+	23.0697i	1.40211	+	1.22962i
$353$	21.3106	+	5.71015i	1.13425	+	0.303921i	0.776636	−	0.629950i	$-0.216925\pi$
$353$	21.3106	+	5.71015i	1.13425	+	0.303921i	0.357611	+	0.933870i	$0.383591\pi$
$354$	10.3716	−	21.0314i	0.551242	−	1.11781i
$355$	−8.80422	−	1.15910i	−0.467279	−	0.0615185i
$356$	−25.9672			−1.37626
$357$	−10.6254	−	2.47014i	−0.562354	−	0.130734i
$358$	−6.36043			−0.336159
$359$	21.8418	+	2.87553i	1.15277	+	0.151765i	0.682586	−	0.730805i	$-0.260855\pi$
$359$	21.8418	+	2.87553i	1.15277	+	0.151765i	0.470181	+	0.882570i	$0.344189\pi$
$360$	1.13761	−	2.30685i	0.0599575	−	0.121582i
$361$	10.6802	+	2.86175i	0.562115	+	0.150618i
$362$	2.62143	+	2.29894i	0.137779	+	0.120829i
$363$	−6.60340	+	9.88268i	−0.346588	+	0.518706i
$364$	27.3689	+	38.7579i	1.43452	+	2.03146i
$365$	1.61216	+	0.667780i	0.0843845	+	0.0349532i
$366$	−16.3925	−	21.3632i	−0.856852	−	1.11667i
$367$	−16.8516	−	19.2156i	−0.879649	−	1.00305i	−0.999947	−	0.0103091i	$-0.996718\pi$
$367$	−16.8516	−	19.2156i	−0.879649	−	1.00305i	0.120298	−	0.992738i	$-0.461615\pi$
$368$	−2.15819	−	0.141455i	−0.112503	−	0.00737385i
$369$	−7.74781	+	8.83468i	−0.403335	+	0.459915i
$370$	−10.6313	+	10.6313i	−0.552695	+	0.552695i
$371$	−5.71975	−	3.61199i	−0.296955	−	0.187525i
$372$	−4.82221	+	1.99742i	−0.250020	+	0.103562i
$373$	−23.0611	−	13.3143i	−1.19406	−	0.689390i	−0.234834	−	0.972035i	$-0.575455\pi$
$373$	−23.0611	−	13.3143i	−1.19406	−	0.689390i	−0.959225	+	0.282645i	$0.908788\pi$
$374$	−43.2188	−	2.50353i	−2.23479	−	0.129454i
$375$	5.69610	+	9.86594i	0.294146	+	0.509475i
$376$	−1.51780	+	11.5288i	−0.0782745	+	0.594554i
$377$	−4.25501	−	6.36807i	−0.219144	−	0.327973i
$378$	0.906174	+	5.73572i	0.0466086	+	0.295013i
$379$	−14.0282	−	2.79039i	−0.720582	−	0.143333i	−0.178841	−	0.983878i	$-0.557235\pi$
$379$	−14.0282	−	2.79039i	−0.720582	−	0.143333i	−0.541741	+	0.840545i	$0.682235\pi$
$380$	−10.2130	+	5.03650i	−0.523917	+	0.258367i
$381$	−5.43265	+	4.76430i	−0.278323	+	0.244083i
$382$	−4.25268	−	32.3023i	−0.217586	−	1.65273i
$383$	5.13090	−	3.93708i	0.262177	−	0.201175i	−0.469305	−	0.883036i	$-0.655496\pi$
$383$	5.13090	−	3.93708i	0.262177	−	0.201175i	0.731482	+	0.681861i	$0.238829\pi$
$384$	12.8967	−	2.56531i	0.658130	−	0.130910i
$385$	11.6135	−	13.9527i	0.591879	−	0.711097i
$386$	1.46828	−	7.38155i	0.0747335	−	0.375711i
$387$	−5.52905	+	1.48150i	−0.281057	+	0.0753091i
$388$	17.7125	+	8.73484i	0.899216	+	0.443444i
$389$	3.68136	+	2.82481i	0.186652	+	0.143223i	0.697861	−	0.716233i	$-0.254135\pi$
$389$	3.68136	+	2.82481i	0.186652	+	0.143223i	−0.511209	+	0.859457i	$0.670802\pi$
$390$	−10.0197	+	17.3546i	−0.507365	+	0.878782i
$391$	4.34391	−	2.95042i	0.219681	−	0.149209i
$392$	−12.2769	−	2.61947i	−0.620079	−	0.132303i
$393$	3.73834	+	9.02515i	0.188574	+	0.455259i
$394$	−0.308807	−	4.71149i	−0.0155575	−	0.237361i
$395$	6.34678	−	23.6865i	0.319341	−	1.19180i
$396$	4.33194	+	12.7615i	0.217688	+	0.641288i
$397$	−4.32056	−	8.76123i	−0.216843	−	0.439714i	0.761086	−	0.648651i	$-0.224666\pi$
$397$	−4.32056	−	8.76123i	−0.216843	−	0.439714i	−0.977929	+	0.208937i	$0.933000\pi$
$398$	7.69008	+	38.6607i	0.385469	+	1.93788i
$399$	3.56053	−	6.55164i	0.178250	−	0.327992i
$400$	−1.91250	+	4.61719i	−0.0956252	+	0.230860i
$401$	20.3216	+	6.89824i	1.01481	+	0.344482i	0.778802	−	0.627269i	$-0.215828\pi$
$401$	20.3216	+	6.89824i	1.01481	+	0.344482i	0.236008	+	0.971751i	$0.424161\pi$
$402$	−1.06769	+	16.2898i	−0.0532514	+	0.812460i
$403$	11.1689	−	3.79132i	0.556362	−	0.188859i
$404$	4.18912	+	15.6340i	0.208416	+	0.777820i
$405$	−1.19255	+	0.796836i	−0.0592582	+	0.0395951i
$406$	6.79255	+	1.63353i	0.337109	+	0.0810706i
$407$		−	22.8487i		−	1.13257i
$408$	−4.83293	+	5.59598i	−0.239265	+	0.277042i
$409$	8.53671	−	4.92867i	0.422113	−	0.243707i	−0.273868	−	0.961767i	$-0.588303\pi$
$409$	8.53671	−	4.92867i	0.422113	−	0.243707i	0.695981	+	0.718060i	$0.254970\pi$
$410$	22.5183	−	29.3464i	1.11210	−	1.44931i
$411$	−3.02600	+	0.198335i	−0.149262	+	0.00978312i
$412$	18.2778	+	18.2778i	0.900481	+	0.900481i
$413$	−6.22801	−	27.5734i	−0.306460	−	1.35680i
$414$	−2.32417	−	1.55296i	−0.114227	−	0.0763239i
$415$	2.97115	−	8.75273i	0.145848	−	0.429655i
$416$	−46.1610	+	6.07721i	−2.26323	+	0.297960i
$417$	−18.7688	+	2.47096i	−0.919113	+	0.121004i
$418$	9.51192	−	28.0212i	0.465243	−	1.37056i
$419$	−0.539090	−	0.360208i	−0.0263363	−	0.0175973i	0.542332	−	0.840164i	$-0.317541\pi$
$419$	−0.539090	−	0.360208i	−0.0263363	−	0.0175973i	−0.568669	+	0.822567i	$0.692541\pi$
$420$	−2.35523	−	10.4273i	−0.114923	−	0.508802i
$421$	20.4073	+	20.4073i	0.994591	+	0.994591i	0.999985	−	0.00539451i	$-0.00171713\pi$
$421$	20.4073	+	20.4073i	0.994591	+	0.994591i	−0.00539451	+	0.999985i	$0.501717\pi$
$422$	−30.1626	+	1.97696i	−1.46829	+	0.0962369i
$423$	3.94734	−	5.14428i	0.191926	−	0.250123i
$424$	−3.97094	+	2.29262i	−0.192846	+	0.111340i
$425$	−3.22930	−	11.6962i	−0.156644	−	0.567348i
$426$		−	13.5889i		−	0.658385i
$427$	−31.5608	−	7.58998i	−1.52733	−	0.367305i
$428$	−16.8202	+	11.2389i	−0.813037	+	0.543254i
$429$	−7.88207	−	29.4163i	−0.380550	−	1.42023i
$430$	17.0626	−	5.79199i	0.822834	−	0.279315i
$431$	1.07759	−	16.4409i	0.0519059	−	0.791930i	−0.889980	−	0.455999i	$-0.849282\pi$
$431$	1.07759	−	16.4409i	0.0519059	−	0.791930i	0.941886	−	0.335932i	$-0.109051\pi$
$432$	−1.60808	−	0.545870i	−0.0773689	−	0.0262632i
$433$	0.756040	−	1.82524i	0.0363330	−	0.0877156i	−0.904671	−	0.426110i	$-0.859884\pi$
$433$	0.756040	−	1.82524i	0.0363330	−	0.0877156i	0.941004	+	0.338394i	$0.109884\pi$
$434$	−5.13741	+	9.45321i	−0.246603	+	0.453768i
$435$	0.336641	+	1.69241i	0.0161407	+	0.0811447i
$436$	20.5675	+	41.7068i	0.985006	+	1.99739i
$437$	1.15378	+	3.39892i	0.0551927	+	0.162593i
$438$	−0.691118	+	2.57929i	−0.0330229	+	0.123243i
$439$	−2.40697	−	36.7233i	−0.114878	−	1.75271i	−0.534648	−	0.845075i	$-0.679556\pi$
$439$	−2.40697	−	36.7233i	−0.114878	−	1.75271i	0.419769	−	0.907631i	$-0.362111\pi$
$440$	−4.70881	−	11.3681i	−0.224484	−	0.541952i
$441$	5.19839	+	4.68794i	0.247542	+	0.223235i
$442$	40.4243	−	41.0424i	1.92279	−	1.95219i
$443$	−18.0511	+	31.2654i	−0.857633	+	1.48546i	0.0165472	+	0.999863i	$0.494733\pi$
$443$	−18.0511	+	31.2654i	−0.857633	+	1.48546i	−0.874180	+	0.485601i	$0.838601\pi$
$444$	−10.6745	−	8.19080i	−0.506587	−	0.388718i
$445$	−11.8573	−	5.84738i	−0.562091	−	0.277192i
$446$	−18.1586	+	4.86560i	−0.859837	+	0.230393i
$447$	3.73222	−	18.7631i	0.176528	−	0.887465i
$448$	21.4212	−	25.7359i	1.01206	−	1.21591i
$449$	−8.97806	+	1.78585i	−0.423701	+	0.0842794i	−0.402335	−	0.915492i	$-0.631801\pi$
$449$	−8.97806	+	1.78585i	−0.423701	+	0.0842794i	−0.0213656	+	0.999772i	$0.506801\pi$
$450$	−5.12426	+	3.93198i	−0.241560	+	0.185355i
$451$	7.33747	+	55.7336i	0.345508	+	2.62439i
$452$	−36.2662	+	31.8046i	−1.70582	+	1.49596i
$453$	−8.34355	+	4.11458i	−0.392014	+	0.193320i
$454$	18.7435	+	3.72831i	0.879676	+	0.174978i
$455$	3.76973	+	23.8609i	0.176728	+	1.11862i
$456$	−2.80796	−	4.20242i	−0.131495	−	0.196796i
$457$	−4.13298	+	31.3931i	−0.193333	+	1.46851i	0.569543	+	0.821961i	$0.307120\pi$
$457$	−4.13298	+	31.3931i	−0.193333	+	1.46851i	−0.762876	+	0.646545i	$0.776213\pi$
$458$	16.3904	+	28.3889i	0.765872	+	1.32653i
$459$	3.89412	−	1.35491i	0.181762	−	0.0632420i
$460$	4.45646	+	2.57294i	0.207783	+	0.119964i
$461$	2.31450	−	0.958695i	0.107797	−	0.0446509i	−0.328133	−	0.944631i	$-0.606420\pi$
$461$	2.31450	−	0.958695i	0.107797	−	0.0446509i	0.435930	+	0.899981i	$0.356420\pi$
$462$	23.4881	+	14.8326i	1.09277	+	0.690076i
$463$	−4.29235	+	4.29235i	−0.199482	+	0.199482i	−0.799778	−	0.600296i	$-0.795050\pi$
$463$	−4.29235	+	4.29235i	−0.199482	+	0.199482i	0.600296	+	0.799778i	$0.295050\pi$
$464$	−1.34711	+	1.53609i	−0.0625382	+	0.0713111i
$465$	−2.65173	−	0.173804i	−0.122971	−	0.00805996i
$466$	−29.5115	−	33.6514i	−1.36709	−	1.55887i
$467$	22.9416	+	29.8981i	1.06161	+	1.38352i	0.919236	+	0.393706i	$0.128807\pi$
$467$	22.9416	+	29.8981i	1.06161	+	1.38352i	0.142375	+	0.989813i	$0.454526\pi$
$468$	−16.5682	−	6.86279i	−0.765867	−	0.317232i
$469$	11.3514	+	16.0751i	0.524159	+	0.742277i
$470$	−11.3401	+	16.9717i	−0.523082	+	0.782847i
$471$	−1.21458	−	1.06516i	−0.0559649	−	0.0490799i
$472$	−18.5075	−	4.95908i	−0.851879	−	0.228260i
$473$	−12.1114	+	24.5596i	−0.556884	+	1.12925i
$474$	37.2039	+	4.89798i	1.70883	+	0.224972i
$475$	8.29404			0.380557
$476$	−0.985340	+	30.7150i	−0.0451630	+	1.40782i
$477$	2.55684			0.117070
$478$	33.5576	+	4.41795i	1.53489	+	0.202072i
$479$	6.56519	−	13.3129i	0.299971	−	0.608281i	−0.693744	−	0.720222i	$-0.744040\pi$
$479$	6.56519	−	13.3129i	0.299971	−	0.608281i	0.993715	+	0.111941i	$0.0357066\pi$
$480$	10.1326	+	2.71501i	0.462486	+	0.123923i
$481$	22.8594	+	20.0472i	1.04230	+	0.914073i
$482$	17.7253	−	26.5277i	0.807363	−	1.20830i
$483$	−3.35559	+	0.307026i	−0.152684	+	0.0139702i
$484$	30.9345	+	12.8135i	1.40612	+	0.582432i
$485$	6.12105	+	7.97711i	0.277943	+	0.362222i
$486$	−1.44712	−	1.65013i	−0.0656428	−	0.0748513i
$487$	15.3533	+	1.00631i	0.695724	+	0.0456002i	0.409162	−	0.912462i	$-0.365821\pi$
$487$	15.3533	+	1.00631i	0.695724	+	0.0456002i	0.286562	+	0.958062i	$0.407488\pi$
$488$	−14.5071	+	16.5421i	−0.656704	+	0.748827i
$489$	8.70449	−	8.70449i	0.393631	−	0.393631i
$490$	−17.2942	−	13.6553i	−0.781271	−	0.616885i
$491$	−24.9811	+	10.3475i	−1.12738	+	0.466977i	−0.866890	−	0.498499i	$-0.833885\pi$
$491$	−24.9811	+	10.3475i	−1.12738	+	0.466977i	−0.260492	+	0.965476i	$0.583885\pi$
$492$	28.6679	+	16.5514i	1.29245	+	0.746196i
$493$	0.286866	−	4.95220i	0.0129198	−	0.223036i
$494$	19.6887	+	34.1018i	0.885836	+	1.53431i
$495$	−0.895593	+	6.80270i	−0.0402539	+	0.305759i
$496$	−1.74807	−	2.61618i	−0.0784909	−	0.117470i
$497$	−10.3040	−	12.7344i	−0.462197	−	0.571218i
$498$	13.8727	+	2.75946i	0.621652	+	0.123654i
$499$	−5.30505	+	2.61616i	−0.237487	+	0.117115i	−0.557138	−	0.830420i	$-0.688101\pi$
$499$	−5.30505	+	2.61616i	−0.237487	+	0.117115i	0.319652	+	0.947535i	$0.396434\pi$
$500$	24.1286	−	21.1603i	1.07907	−	0.946315i
$501$	0.122515	+	0.930591i	0.00547355	+	0.0415757i
$502$	−8.93948	+	6.85950i	−0.398988	+	0.306155i
$503$	−20.5868	+	4.09497i	−0.917920	+	0.182586i	−0.631372	−	0.775480i	$-0.717508\pi$
$503$	−20.5868	+	4.09497i	−0.917920	+	0.182586i	−0.286548	+	0.958066i	$0.592508\pi$
$504$	4.45206	−	1.64050i	0.198311	−	0.0730735i
$505$	−1.60765	+	8.08221i	−0.0715396	+	0.359654i
$506$	−12.9166	+	3.46100i	−0.574213	+	0.153860i
$507$	24.6863	+	12.1740i	1.09636	+	0.540664i
$508$	16.1493	+	12.3918i	0.716508	+	0.549796i
$509$	−9.26782	+	16.0523i	−0.410789	+	0.711507i	−0.994976	−	0.100112i	$-0.968080\pi$
$509$	−9.26782	+	16.0523i	−0.410789	+	0.711507i	0.584187	+	0.811619i	$0.301413\pi$
$510$	−11.9531	+	5.05775i	−0.529294	+	0.223961i
$511$	1.30812	+	2.94115i	0.0578680	+	0.130109i
$512$	7.08396	+	17.1022i	0.313070	+	0.755817i
$513$	0.184328	+	2.81231i	0.00813830	+	0.124166i
$514$	6.49476	−	24.2388i	0.286472	−	1.06913i
$515$	4.23026	+	12.4620i	0.186408	+	0.549139i
$516$	7.13201	+	14.4623i	0.313969	+	0.636667i
$517$	−6.05169	−	30.4239i	−0.266153	−	1.33804i
$518$	−27.7253	+	0.715281i	−1.21818	+	0.0314276i
$519$	1.02465	−	2.47372i	0.0449770	−	0.108584i
$520$	15.5049	+	5.26319i	0.679933	+	0.230806i
$521$	0.350239	−	5.34361i	0.0153442	−	0.234108i	−0.983298	−	0.182005i	$-0.941741\pi$
$521$	0.350239	−	5.34361i	0.0153442	−	0.234108i	0.998642	−	0.0521023i	$-0.0165922\pi$
$522$	−2.50041	+	0.848774i	−0.109440	+	0.0371498i
$523$	11.5088	+	42.9514i	0.503245	+	1.87814i	0.477818	+	0.878459i	$0.341428\pi$
$523$	11.5088	+	42.9514i	0.503245	+	1.87814i	0.0254265	+	0.999677i	$0.491906\pi$
$524$	22.8815	−	15.2890i	0.999585	−	0.667901i
$525$	−1.82056	+	7.57029i	−0.0794559	+	0.330395i
$526$			30.6142i			1.33484i
$527$	7.25234	+	2.40062i	0.315917	+	0.104573i
$528$	−7.03565	+	4.06203i	−0.306187	+	0.176777i
$529$	−13.0141	+	16.9603i	−0.565830	+	0.737404i
$530$	−8.03146	+	0.526410i	−0.348864	+	0.0228658i
$531$	7.55494	+	7.55494i	0.327856	+	0.327856i
$532$	−20.0587	−	6.23690i	−0.869655	−	0.270404i
$533$	−62.1975	−	41.5590i	−2.69407	−	1.80012i
$534$	6.50305	−	19.1574i	0.281414	−	0.829020i
$535$	−10.2114	+	1.34435i	−0.441477	+	0.0581215i
$536$	13.2246	−	1.74105i	0.571214	−	0.0752017i
$537$	0.931522	−	2.74418i	0.0401982	−	0.118420i
$538$	−4.59532	−	3.07049i	−0.198118	−	0.132378i
$539$	33.2583	−	3.91029i	1.43254	−	0.168428i
$540$	2.85703	+	2.85703i	0.122947	+	0.122947i
$541$	28.6394	−	1.87712i	1.23130	−	0.0807038i	0.564180	−	0.825652i	$-0.309193\pi$
$541$	28.6394	−	1.87712i	1.23130	−	0.0807038i	0.667122	+	0.744948i	$0.267526\pi$
$542$	14.2878	−	18.6203i	0.613715	−	0.799809i
$543$	−1.37579	+	0.794312i	−0.0590408	+	0.0340872i
$544$	−26.2293	−	14.8793i	−1.12457	−	0.637944i
$545$			23.6759i			1.01416i
$546$	−35.4478	+	10.4852i	−1.51702	+	0.448725i
$547$	17.1057	−	11.4296i	0.731385	−	0.488696i	−0.133259	−	0.991081i	$-0.542544\pi$
$547$	17.1057	−	11.4296i	0.731385	−	0.488696i	0.864644	+	0.502385i	$0.167544\pi$
$548$	2.21104	+	8.25170i	0.0944508	+	0.352495i
$549$	11.6178	−	3.94372i	0.495837	−	0.168314i
$550$	−2.02091	+	30.8331i	−0.0861717	+	1.31473i
$551$	3.21079	+	1.08992i	0.136784	+	0.0464321i
$552$	−0.874034	+	2.11010i	−0.0372013	+	0.0898120i
$553$	38.5785	−	23.6204i	1.64052	−	1.00444i
$554$	−5.62565	−	28.2821i	−0.239011	−	1.20159i
$555$	−3.02981	−	6.14384i	−0.128608	−	0.260792i
$556$	17.1422	+	50.4994i	0.726993	+	2.14165i
$557$	0.216709	−	0.808769i	0.00918225	−	0.0342686i	−0.961183	−	0.275913i	$-0.911020\pi$
$557$	0.216709	−	0.808769i	0.00918225	−	0.0342686i	0.970365	+	0.241644i	$0.0776866\pi$
$558$	−0.265963	−	4.05781i	−0.0112591	−	0.171781i
$559$	−13.9446	−	33.6653i	−0.589795	−	1.42389i
$560$	5.88808	−	2.61882i	0.248817	−	0.110665i
$561$	7.40978	−	18.2799i	0.312841	−	0.771777i
$562$	31.4201	−	54.4212i	1.32538	−	2.29562i
$563$	2.25000	+	1.72648i	0.0948260	+	0.0727626i	0.655086	−	0.755554i	$-0.272632\pi$
$563$	2.25000	+	1.72648i	0.0948260	+	0.0727626i	−0.560260	+	0.828317i	$0.689299\pi$
$564$	−16.3828	−	8.07910i	−0.689840	−	0.340192i
$565$	−23.7219	+	6.35628i	−0.997990	+	0.267411i
$566$	−1.74767	+	8.78612i	−0.0734600	+	0.369308i
$567$	−2.60736	−	0.449065i	−0.109499	−	0.0188590i
$568$	−10.8899	+	2.16614i	−0.456931	+	0.0908893i
$569$	8.70847	−	6.68225i	0.365078	−	0.280134i	−0.409889	−	0.912135i	$-0.634433\pi$
$569$	8.70847	−	6.68225i	0.365078	−	0.280134i	0.774968	+	0.632001i	$0.217766\pi$
$570$	−1.15801	−	8.79598i	−0.0485038	−	0.368423i
$571$	−23.2613	+	20.3996i	−0.973456	+	0.853698i	−0.989258	−	0.146177i	$-0.953303\pi$
$571$	−23.2613	+	20.3996i	−0.973456	+	0.853698i	0.0158020	+	0.999875i	$0.494970\pi$
$572$	−76.9440	+	37.9446i	−3.21719	+	1.58654i
$573$	14.5595	+	2.89607i	0.608233	+	0.120985i
$574$	67.3990	−	10.6482i	2.81318	−	0.444448i
$575$	−2.08229	−	3.11637i	−0.0868375	−	0.129961i
$576$	−1.65193	+	12.5476i	−0.0688303	+	0.522818i
$577$	12.9711	+	22.4666i	0.539994	+	0.935297i	0.998904	+	0.0468141i	$0.0149069\pi$
$577$	12.9711	+	22.4666i	0.539994	+	0.935297i	−0.458910	+	0.888483i	$0.651760\pi$
$578$	36.9140	−	5.43089i	1.53542	−	0.225895i
$579$	2.96970	+	1.71455i	0.123416	+	0.0712545i
$580$	4.49103	−	1.86024i	0.186480	−	0.0772425i
$581$	15.0928	−	7.93326i	0.626155	−	0.329127i
$582$	−10.8799	+	10.8799i	−0.450988	+	0.450988i
$583$	8.06491	−	9.19627i	0.334015	−	0.380871i
$584$	2.17717	+	0.142699i	0.0900918	+	0.00590493i
$585$	−6.02011	−	6.86462i	−0.248901	−	0.283817i
$586$	20.6917	+	26.9659i	0.854765	+	1.11395i
$587$	−21.6435	−	8.96502i	−0.893322	−	0.370026i	−0.111673	−	0.993745i	$-0.535621\pi$
$587$	−21.6435	−	8.96502i	−0.893322	−	0.370026i	−0.781649	+	0.623719i	$0.785621\pi$
$588$	10.0956	−	16.9393i	0.416335	−	0.698566i
$589$	−2.90111	+	4.34181i	−0.119538	+	0.178901i
$590$	−25.2868	−	22.1759i	−1.04104	−	0.912967i
$591$	2.07798	+	0.556792i	0.0854765	+	0.0229034i
$592$	3.58736	−	7.27445i	0.147440	−	0.298978i
$593$	19.0503	+	2.50802i	0.782304	+	0.102992i	0.511090	−	0.859527i	$-0.329242\pi$
$593$	19.0503	+	2.50802i	0.782304	+	0.102992i	0.271213	+	0.962519i	$0.412575\pi$
$594$	−10.4997			−0.430806
$595$	−7.36642	+	13.8034i	−0.301994	+	0.565883i
$596$	−53.8928			−2.20754
$597$	−17.8062	−	2.34423i	−0.728760	−	0.0959431i
$598$	7.87025	−	15.9593i	0.321838	−	0.652624i
$599$	40.3733	+	10.8180i	1.64961	+	0.442011i	0.959503	−	0.281697i	$-0.0908973\pi$
$599$	40.3733	+	10.8180i	1.64961	+	0.442011i	0.690106	+	0.723708i	$0.257564\pi$
$600$	3.96786	+	3.47972i	0.161987	+	0.142059i
$601$	−4.68618	+	7.01337i	−0.191153	+	0.286081i	−0.914650	−	0.404247i	$-0.867534\pi$
$601$	−4.68618	+	7.01337i	−0.191153	+	0.286081i	0.723497	+	0.690328i	$0.242534\pi$
$602$	30.1804	+	13.9275i	1.23006	+	0.567642i
$603$	−6.87177	−	2.84638i	−0.279840	−	0.115914i
$604$	15.9539	+	20.7915i	0.649155	+	0.845996i
$605$	11.2401	+	12.8169i	0.456977	+	0.521082i
$606$	−12.5831	−	0.824740i	−0.511154	−	0.0335028i
$607$	−21.9400	+	25.0177i	−0.890516	+	1.01544i	0.109255	+	0.994014i	$0.465154\pi$
$607$	−21.9400	+	25.0177i	−0.890516	+	1.01544i	−0.999770	+	0.0214246i	$0.993180\pi$
$608$	14.5755	−	14.5755i	0.591116	−	0.591116i
$609$	−1.69959	+	2.69138i	−0.0688708	+	0.109060i
$610$	−35.6816	+	14.7798i	−1.44471	+	0.598417i
$611$	35.7478	+	20.6390i	1.44620	+	0.834964i
$612$	−5.88372	−	10.0146i	−0.237835	−	0.404818i
$613$	−1.05820	−	1.83286i	−0.0427404	−	0.0740286i	0.843864	−	0.536557i	$-0.180276\pi$
$613$	−1.05820	−	1.83286i	−0.0427404	−	0.0740286i	−0.886604	+	0.462529i	$0.846942\pi$
$614$	6.13268	−	46.5824i	0.247495	−	1.87991i
$615$	9.36342	+	14.0133i	0.377569	+	0.565073i
$616$	8.14249	−	21.1874i	0.328070	−	0.853666i
$617$	22.2715	+	4.43007i	0.896616	+	0.178348i	0.621825	−	0.783156i	$-0.286391\pi$
$617$	22.2715	+	4.43007i	0.896616	+	0.178348i	0.274791	+	0.961504i	$0.411391\pi$
$618$	−18.0618	+	8.90710i	−0.726553	+	0.358296i
$619$	−34.5510	+	30.3004i	−1.38872	+	1.21788i	−0.441513	+	0.897255i	$0.645558\pi$
$619$	−34.5510	+	30.3004i	−1.38872	+	1.21788i	−0.947208	+	0.320620i	$0.896109\pi$
$620$	0.977143	+	7.42214i	0.0392430	+	0.298080i
$621$	1.01041	−	0.775312i	0.0405462	−	0.0311122i
$622$	−19.2456	+	3.82819i	−0.771679	+	0.153496i
$623$	−8.43222	−	22.8838i	−0.337830	−	0.916820i
$624$	2.10905	−	10.6029i	0.0844296	−	0.424456i
$625$	1.56969	−	0.420597i	0.0627876	−	0.0168239i
$626$	−25.2639	−	12.4588i	−1.00975	−	0.497952i
$627$	10.6965	+	8.20775i	0.427179	+	0.327786i
$628$	−2.27547	+	3.94123i	−0.0908011	+	0.157272i
$629$	3.98828	+	19.2845i	0.159023	+	0.768925i
$630$	8.28262	+	0.873777i	0.329987	+	0.0348121i
$631$	−7.89021	−	19.0487i	−0.314104	−	0.758315i	−0.999544	−	0.0301859i	$-0.990390\pi$
$631$	−7.89021	−	19.0487i	−0.314104	−	0.758315i	0.685440	−	0.728129i	$-0.259610\pi$
$632$	−2.00532	−	30.5953i	−0.0797675	−	1.21702i
$633$	3.56454	−	13.3030i	0.141678	−	0.528749i
$634$	7.24159	+	21.3330i	0.287600	+	0.847243i
$635$	4.58376	+	9.29495i	0.181901	+	0.368859i
$636$	−1.40520	−	7.06443i	−0.0557199	−	0.280123i
$637$	−25.2683	+	36.7047i	−1.00117	+	1.45429i
$638$	−4.83410	+	11.6705i	−0.191384	+	0.462041i
$639$	5.86287	+	1.99018i	0.231932	+	0.0787302i
$640$	1.23348	−	18.8193i	0.0487575	−	0.743896i
$641$	−14.3644	+	4.87607i	−0.567361	+	0.192593i	−0.590357	−	0.807142i	$-0.701013\pi$
$641$	−14.3644	+	4.87607i	−0.567361	+	0.192593i	0.0229957	+	0.999736i	$0.492680\pi$
$642$	−4.07919	−	15.2238i	−0.160993	−	0.600834i
$643$	9.96515	−	6.65850i	0.392987	−	0.262586i	−0.343340	−	0.939211i	$-0.611558\pi$
$643$	9.96515	−	6.65850i	0.392987	−	0.262586i	0.736327	+	0.676625i	$0.236558\pi$
$644$	2.69248	+	9.10259i	0.106099	+	0.358692i
$645$			8.20987i			0.323263i
$646$	−3.13700	+	25.3105i	−0.123424	+	0.995827i
$647$	14.7493	−	8.51551i	0.579855	−	0.334779i	−0.181221	−	0.983442i	$-0.558005\pi$
$647$	14.7493	−	8.51551i	0.579855	−	0.334779i	0.761076	+	0.648663i	$0.224672\pi$
$648$	−1.09171	+	1.42274i	−0.0428863	+	0.0558905i
$649$	51.0033	−	3.34293i	2.00205	−	0.131222i
$650$	−29.0744	−	29.0744i	−1.14039	−	1.14039i
$651$	−3.32614	−	3.60099i	−0.130362	−	0.141134i
$652$	−28.8340	−	19.2662i	−1.12923	−	0.754525i
$653$	3.93248	−	11.5847i	0.153890	−	0.453345i	−0.842455	−	0.538767i	$-0.818890\pi$
$653$	3.93248	−	11.5847i	0.153890	−	0.453345i	0.996345	+	0.0854218i	$0.0272238\pi$
$654$	−35.9201	+	4.72897i	−1.40459	+	0.184917i
$655$	13.8911	−	1.82880i	0.542771	−	0.0714572i
$656$	−6.41438	+	18.8962i	−0.250440	+	0.737771i
$657$	−1.01160	−	0.675932i	−0.0394664	−	0.0263706i
$658$	−36.7277	+	8.29570i	−1.43179	+	0.323400i
$659$	−18.3302	−	18.3302i	−0.714043	−	0.714043i	0.253336	−	0.967378i	$-0.418472\pi$
$659$	−18.3302	−	18.3302i	−0.714043	−	0.714043i	−0.967378	+	0.253336i	$0.918472\pi$
$660$	19.2878	−	1.26419i	0.750775	−	0.0492084i
$661$	−0.394575	+	0.514220i	−0.0153472	+	0.0200008i	−0.800964	−	0.598713i	$-0.795679\pi$
$661$	−0.394575	+	0.514220i	−0.0153472	+	0.0200008i	0.785617	+	0.618713i	$0.212346\pi$
$662$	26.8516	−	15.5028i	1.04362	−	0.602533i
$663$	11.7872	+	23.4518i	0.457776	+	0.910791i
$664$		−	11.5573i		−	0.448508i
$665$	−7.75489	−	7.36481i	−0.300722	−	0.285595i
$666$	8.71601	−	5.82385i	0.337739	−	0.225670i
$667$	−0.396576	−	1.48004i	−0.0153555	−	0.0573075i
$668$	2.50385	−	0.849942i	0.0968768	−	0.0328852i
$669$	0.560204	−	8.54706i	0.0216587	−	0.330448i
$670$	22.1714	+	7.52618i	0.856557	+	0.290762i
$671$	22.4610	−	54.2258i	0.867099	−	2.09336i
$672$	10.1043	+	16.5030i	0.389781	+	0.636618i
$673$	1.79449	+	9.02149i	0.0691723	+	0.347753i	0.999836	−	0.0181237i	$-0.00576926\pi$
$673$	1.79449	+	9.02149i	0.0691723	+	0.347753i	−0.930663	+	0.365876i	$0.880769\pi$
$674$	4.29537	+	8.71015i	0.165452	+	0.335503i
$675$	−0.945958	−	2.78670i	−0.0364099	−	0.107260i
$676$	20.0688	−	74.8979i	0.771878	−	2.88069i
$677$	0.879087	+	13.4123i	0.0337861	+	0.515476i	0.980892	+	0.194554i	$0.0623260\pi$
$677$	0.879087	+	13.4123i	0.0337861	+	0.515476i	−0.947106	+	0.320922i	$0.896007\pi$
$678$	−14.3816	−	34.7203i	−0.552323	−	1.33343i
$679$	−1.94593	+	18.4457i	−0.0746781	+	0.707881i
$680$	5.95859	+	8.77283i	0.228502	+	0.336423i
$681$	−4.35366	+	7.54076i	−0.166833	+	0.288963i
$682$	−15.4338	−	11.8428i	−0.590990	−	0.453483i
$683$	41.9176	+	20.6715i	1.60393	+	0.790973i	0.999982	−	0.00604761i	$-0.00192502\pi$
$683$	41.9176	+	20.6715i	1.60393	+	0.790973i	0.603952	+	0.797020i	$0.293592\pi$
$684$	7.66898	−	2.05490i	0.293231	−	0.0785709i
$685$	−0.848527	+	4.26583i	−0.0324205	+	0.162989i
$686$	−5.78601	−	40.2341i	−0.220911	−	1.53614i
$687$	−14.6487	+	2.91382i	−0.558885	+	0.111169i
$688$	−7.71194	+	5.91758i	−0.294015	+	0.225606i
$689$	2.12453	+	16.1374i	0.0809380	+	0.614785i
$690$	−3.01423	+	2.64341i	−0.114750	+	0.100633i
$691$	−2.29372	+	1.13114i	−0.0872571	+	0.0430305i	−0.485394	−	0.874296i	$-0.661324\pi$
$691$	−2.29372	+	1.13114i	−0.0872571	+	0.0430305i	0.398137	+	0.917326i	$0.369657\pi$
$692$	−7.39790	−	1.47153i	−0.281226	−	0.0559394i
$693$	−9.83945	+	7.96153i	−0.373770	+	0.302433i
$694$	−35.6282	−	53.3213i	−1.35243	−	2.02405i
$695$	−3.54402	+	26.9195i	−0.134432	+	1.02111i
$696$	1.07877	+	1.86849i	0.0408907	+	0.0708248i
$697$	−15.9213	−	45.7589i	−0.603061	−	1.73324i
$698$	−22.1553	−	12.7913i	−0.838589	−	0.484159i
$699$	18.8409	−	7.80414i	0.712627	−	0.295180i
$700$	21.9169	+	0.869609i	0.828382	+	0.0328681i
$701$	0.315883	−	0.315883i	0.0119307	−	0.0119307i	−0.701116	−	0.713047i	$-0.747315\pi$
$701$	0.315883	−	0.315883i	0.0119307	−	0.0119307i	0.713047	+	0.701116i	$0.247315\pi$
$702$	9.21226	−	10.5046i	0.347694	−	0.396470i
$703$	−13.4320	−	0.880383i	−0.506599	−	0.0332043i
$704$	39.9199	+	45.5200i	1.50454	+	1.71560i
$705$	−5.66154	−	7.37826i	−0.213226	−	0.277881i
$706$	44.7362	+	18.5303i	1.68367	+	0.697398i
$707$	−12.4173	+	8.76845i	−0.466999	+	0.329771i
$708$	16.7219	−	25.0260i	0.628446	−	0.940536i
$709$	−31.1258	−	27.2966i	−1.16895	−	1.02514i	−0.999213	−	0.0396551i	$-0.987374\pi$
$709$	−31.1258	−	27.2966i	−1.16895	−	1.02514i	−0.169739	−	0.985489i	$-0.554293\pi$
$710$	−18.8260	−	5.04441i	−0.706527	−	0.189313i
$711$	−7.56194	+	15.3341i	−0.283595	+	0.575073i
$712$	−16.3890	−	2.15766i	−0.614205	−	0.0808616i
$713$	2.35972			0.0883722
$714$	−22.4133	−	8.41897i	−0.838795	−	0.315072i
$715$	−43.6791			−1.63351
$716$	−8.09399	−	1.06559i	−0.302486	−	0.0398231i
$717$	−6.82082	+	13.8313i	−0.254728	+	0.516538i
$718$	46.7042	+	12.5144i	1.74299	+	0.467032i
$719$	19.1877	+	16.8272i	0.715580	+	0.627547i	0.937689	−	0.347475i	$-0.112961\pi$
$719$	19.1877	+	16.8272i	0.715580	+	0.627547i	−0.222109	+	0.975022i	$0.571294\pi$
$720$	−1.35319	+	2.02519i	−0.0504305	+	0.0754745i
$721$	−10.1722	+	22.0427i	−0.378831	+	0.820912i
$722$	22.4204	+	9.28682i	0.834400	+	0.345620i
$723$	8.84929	+	11.5326i	0.329109	+	0.428903i
$724$	2.95076	+	3.36470i	0.109664	+	0.125048i
$725$	−3.53299	−	0.231564i	−0.131212	−	0.00860009i
$726$	−17.2002	+	19.6131i	−0.638360	+	0.727910i
$727$	−8.74718	+	8.74718i	−0.324415	+	0.324415i	−0.850458	−	0.526043i	$-0.823675\pi$
$727$	−8.74718	+	8.74718i	−0.324415	+	0.324415i	0.526043	+	0.850458i	$0.323675\pi$
$728$	14.0532	+	26.7359i	0.520847	+	0.990897i
$729$	0.923880	−	0.382683i	0.0342178	−	0.0141735i
$730$	3.31678	+	1.91494i	0.122759	+	0.0708752i
$731$	5.93525	−	22.8425i	0.219523	−	0.844862i
$732$	−17.2813	−	29.9321i	−0.638736	−	1.10632i
$733$	−0.190752	+	1.44890i	−0.00704558	+	0.0535165i	−0.994606	−	0.103720i	$-0.966925\pi$
$733$	−0.190752	+	1.44890i	−0.00704558	+	0.0535165i	0.987561	+	0.157237i	$0.0502586\pi$
$734$	−31.1645	−	46.6410i	−1.15030	−	1.72155i
$735$	8.42437	−	5.46159i	0.310737	−	0.201454i
$736$	−9.13586	−	1.81724i	−0.336752	−	0.0669842i
$737$	−31.9130	+	15.7377i	−1.17553	+	0.579707i
$738$	−19.3902	+	17.0048i	−0.713764	+	0.625954i
$739$	−2.99936	−	22.7824i	−0.110333	−	0.838065i	−0.953707	−	0.300737i	$-0.902767\pi$
$739$	−2.99936	−	22.7824i	−0.110333	−	0.838065i	0.843374	−	0.537328i	$-0.180566\pi$
$740$	−15.3100	+	11.7478i	−0.562807	+	0.431857i
$741$	−17.5966	+	3.50018i	−0.646427	+	0.128582i
$742$	−11.4115	−	9.49829i	−0.418928	−	0.348693i
$743$	0.231547	−	1.16406i	0.00849462	−	0.0427054i	−0.976306	−	0.216397i	$-0.930570\pi$
$743$	0.231547	−	1.16406i	0.00849462	−	0.0427054i	0.984800	+	0.173691i	$0.0555695\pi$
$744$	−3.20947	+	0.859975i	−0.117665	+	0.0315282i
$745$	−24.6089	−	12.1358i	−0.901600	−	0.444620i
$746$	−46.3669	−	35.5786i	−1.69761	−	1.30263i
$747$	−3.22230	+	5.58118i	−0.117898	+	0.204205i
$748$	−54.5788	−	10.4265i	−1.99560	−	0.381232i
$749$	−15.3663	−	11.1734i	−0.561474	−	0.408267i
$750$	9.56841	+	23.1002i	0.349389	+	0.843499i
$751$	−3.19131	−	48.6899i	−0.116452	−	1.77672i	−0.512692	−	0.858573i	$-0.671352\pi$
$751$	−3.19131	−	48.6899i	−0.116452	−	1.77672i	0.396239	−	0.918147i	$-0.370315\pi$
$752$	2.84999	−	10.6363i	0.103929	−	0.387867i
$753$	−1.65026	−	4.86151i	−0.0601389	−	0.177163i
$754$	−7.43464	−	15.0760i	−0.270753	−	0.549034i
$755$	2.60307	+	13.0865i	0.0947354	+	0.476267i
$756$	0.192223	+	7.45082i	0.00699108	+	0.270984i
$757$	18.4981	−	44.6584i	0.672325	−	1.62314i	−0.105325	−	0.994438i	$-0.533588\pi$
$757$	18.4981	−	44.6584i	0.672325	−	1.62314i	0.777650	−	0.628698i	$-0.216412\pi$
$758$	−29.7262	−	10.0907i	−1.07970	−	0.366510i
$759$	0.398484	−	6.07970i	0.0144641	−	0.220679i
$760$	−6.86437	+	2.33014i	−0.248997	+	0.0845230i
$761$	−3.06598	−	11.4424i	−0.111142	−	0.414787i	0.887828	−	0.460176i	$-0.152214\pi$
$761$	−3.06598	−	11.4424i	−0.111142	−	0.414787i	−0.998969	+	0.0453893i	$0.985547\pi$
$762$	−13.1864	+	8.81084i	−0.477691	+	0.319183i
$763$	−30.0756	+	31.6685i	−1.08881	+	1.14648i
$764$		−	41.8190i		−	1.51296i
$765$	−0.431532	−	5.89787i	−0.0156021	−	0.213238i
$766$	12.2928	−	7.09723i	0.444156	−	0.256433i
$767$	−41.4051	+	53.9602i	−1.49505	+	1.94839i
$768$	3.54053	−	0.232058i	0.127758	−	0.00837368i
$769$	2.46617	+	2.46617i	0.0889322	+	0.0889322i	0.750173	−	0.661241i	$-0.229970\pi$
$769$	2.46617	+	2.46617i	0.0889322	+	0.0889322i	−0.661241	+	0.750173i	$0.729970\pi$
$770$	29.2682	−	27.0343i	1.05475	−	0.974247i
$771$	9.50652	+	6.35205i	0.342369	+	0.228764i
$772$	3.10513	−	9.14743i	0.111756	−	0.329223i
$773$	51.2363	−	6.74539i	1.84284	−	0.242615i	0.873239	−	0.487293i	$-0.162016\pi$
$773$	51.2363	−	6.74539i	1.84284	−	0.242615i	0.969604	+	0.244678i	$0.0786823\pi$
$774$	−12.4557	+	1.63982i	−0.447710	+	0.0589421i
$775$	1.75268	−	5.16323i	0.0629581	−	0.185469i
$776$	10.4533	+	6.98469i	0.375253	+	0.250736i
$777$	3.75193	−	12.0667i	0.134600	−	0.432890i
$778$	7.20143	+	7.20143i	0.258184	+	0.258184i
$779$	33.0467	−	2.16600i	1.18402	−	0.0776049i
$780$	−15.6581	+	20.4060i	−0.560648	+	0.730651i
$781$	25.6511	−	14.8097i	0.917869	−	0.529932i
$782$	10.2976	−	5.17572i	0.368242	−	0.185083i
$783$		−	1.20310i		−	0.0429952i
$784$	11.2025	+	3.97678i	0.400090	+	0.142028i
$785$	−1.92654	+	1.28727i	−0.0687611	+	0.0459447i
$786$	5.54916	+	20.7098i	0.197932	+	0.738693i
$787$	25.9371	−	8.80446i	0.924558	−	0.313845i	0.181746	−	0.983346i	$-0.441825\pi$
$787$	25.9371	−	8.80446i	0.924558	−	0.313845i	0.742812	+	0.669501i	$0.233492\pi$
$788$	0.396365	−	6.04736i	0.0141199	−	0.215428i
$789$	−13.2084	−	4.48364i	−0.470230	−	0.159622i
$790$	20.5963	−	49.7238i	0.732783	−	1.76909i
$791$	−39.8046	−	21.6321i	−1.41529	−	0.769147i
$792$	1.67370	+	8.41426i	0.0594723	+	0.298988i
$793$	34.5441	+	70.0485i	1.22670	+	2.48750i
$794$	−6.89169	−	20.3023i	−0.244577	−	0.720500i
$795$	0.949138	−	3.54223i	0.0336625	−	0.125630i
$796$	3.30904	+	50.4861i	0.117286	+	1.78943i
$797$	9.41368	+	22.7266i	0.333450	+	0.805018i	0.998313	+	0.0580539i	$0.0184895\pi$
$797$	9.41368	+	22.7266i	0.333450	+	0.805018i	−0.664864	+	0.746965i	$0.731510\pi$
$798$	9.62464	−	13.2364i	0.340709	−	0.468564i
$799$	10.4182	+	24.6217i	0.368569	+	0.871053i
$800$	−10.7619	+	18.6401i	−0.380490	+	0.659028i
$801$	7.31295	+	5.61142i	0.258390	+	0.198270i
$802$	42.2437	+	20.8323i	1.49168	+	0.735614i
$803$	−5.62200	+	1.50641i	−0.198396	+	0.0531600i
$804$	−4.08779	+	20.5507i	−0.144165	+	0.724768i
$805$	−0.820293	+	4.76278i	−0.0289115	+	0.167866i
$806$	25.3897	−	5.05033i	0.894315	−	0.177890i
$807$	1.99776	−	1.53294i	0.0703245	−	0.0539619i
$808$	1.34488	+	10.2154i	0.0473127	+	0.359375i
$809$	−36.2675	+	31.8057i	−1.27510	+	1.11823i	−0.288080	+	0.957606i	$0.593017\pi$
$809$	−36.2675	+	31.8057i	−1.27510	+	1.11823i	−0.987016	+	0.160623i	$0.948650\pi$
$810$	−2.82327	+	1.39228i	−0.0991997	+	0.0489199i
$811$	29.4063	+	5.84927i	1.03259	+	0.205396i	0.682169	−	0.731195i	$-0.261037\pi$
$811$	29.4063	+	5.84927i	1.03259	+	0.205396i	0.350426	+	0.936591i	$0.386037\pi$
$812$	8.37022	+	3.21674i	0.293737	+	0.112885i
$813$	5.94109	+	8.89147i	0.208363	+	0.311837i
$814$	6.54564	−	49.7191i	0.229425	−	1.74265i
$815$	−8.82792	−	15.2904i	−0.309228	−	0.535599i
$816$	5.22911	−	4.65647i	0.183056	−	0.163009i
$817$	13.9711	+	8.06622i	0.488787	+	0.282201i
$818$	19.9879	−	8.27927i	0.698861	−	0.289478i
$819$	0.667748	−	16.8294i	0.0233330	−	0.588067i
$820$	33.5722	−	33.5722i	1.17239	−	1.17239i
$821$	−5.82409	+	6.64110i	−0.203262	+	0.231776i	−0.844486	−	0.535578i	$-0.820094\pi$
$821$	−5.82409	+	6.64110i	−0.203262	+	0.231776i	0.641224	+	0.767354i	$0.278427\pi$
$822$	−6.64142	−	0.435302i	−0.231646	−	0.0151829i
$823$	−23.5856	−	26.8943i	−0.822143	−	0.937475i	0.176762	−	0.984254i	$-0.443438\pi$
$823$	−23.5856	−	26.8943i	−0.822143	−	0.937475i	−0.998905	+	0.0467790i	$0.985104\pi$
$824$	10.0172	+	13.0546i	0.348964	+	0.454779i
$825$	−13.0068	−	5.38760i	−0.452839	−	0.187572i
$826$	−5.65306	−	61.7841i	−0.196695	−	2.14974i
$827$	−19.4933	+	29.1739i	−0.677850	+	1.01447i	0.319901	+	0.947451i	$0.396350\pi$
$827$	−19.4933	+	29.1739i	−0.677850	+	1.01447i	−0.997751	+	0.0670233i	$0.978650\pi$
$828$	−2.69746	−	2.36561i	−0.0937432	−	0.0822105i
$829$	−41.5643	−	11.1371i	−1.44359	−	0.386808i	−0.549800	−	0.835296i	$-0.685296\pi$
$829$	−41.5643	−	11.1371i	−1.44359	−	0.386808i	−0.893789	+	0.448488i	$0.851963\pi$
$830$	8.97271	−	18.1949i	0.311447	−	0.631553i
$831$	13.0261	+	1.71491i	0.451869	+	0.0594897i
$832$	−80.5665			−2.79314
$833$	−27.3877	+	9.10560i	−0.948929	+	0.315490i
$834$	−41.5490			−1.43872
$835$	1.33472	+	0.175719i	0.0461897	+	0.00608099i
$836$	16.7990	−	34.0649i	0.581004	−	1.17816i
$837$	1.78968	+	0.479542i	0.0618603	+	0.0165754i
$838$	−1.06987	−	0.938253i	−0.0369581	−	0.0324114i
$839$	14.6184	−	21.8779i	0.504682	−	0.755310i	−0.488414	−	0.872612i	$-0.662424\pi$
$839$	14.6184	−	21.8779i	0.504682	−	0.755310i	0.993096	+	0.117302i	$0.0374245\pi$
$840$	−0.620061	−	6.77684i	−0.0213941	−	0.233823i
$841$	25.4552	+	10.5439i	0.877767	+	0.363583i
$842$	38.5602	+	50.2527i	1.32887	+	1.73182i
$843$	18.8781	+	21.5264i	0.650197	+	0.741408i
$844$	−38.7147	−	2.53750i	−1.33262	−	0.0873443i
$845$	26.0297	−	29.6812i	0.895448	−	1.02106i
$846$	10.0632	−	10.0632i	0.345979	−	0.345979i
$847$	−1.24675	+	31.4222i	−0.0428389	+	1.07968i
$848$	4.01152	−	1.66163i	0.137756	−	0.0570605i
$849$	−3.53478	−	2.04080i	−0.121313	−	0.0700402i
$850$	−3.67629	−	26.3761i	−0.126096	−	0.904694i
$851$	3.04144	+	5.26792i	0.104259	+	0.180582i
$852$	2.27662	−	17.2926i	0.0779956	−	0.592435i
$853$	28.8251	+	43.1397i	0.986951	+	1.47708i	0.875448	+	0.483313i	$0.160567\pi$
$853$	28.8251	+	43.1397i	0.986951	+	1.47708i	0.111503	+	0.993764i	$0.464433\pi$
$854$	−66.5021	−	25.5573i	−2.27566	−	0.874553i
$855$	3.96458	+	0.788605i	0.135586	+	0.0269697i
$856$	−11.5498	+	5.69575i	−0.394765	+	0.194677i
$857$	33.6921	−	29.5472i	1.15090	−	1.00931i	0.151117	−	0.988516i	$-0.451713\pi$
$857$	33.6921	−	29.5472i	1.15090	−	1.00931i	0.999784	−	0.0207973i	$-0.00662045\pi$
$858$	−8.72437	−	66.2681i	−0.297845	−	2.26236i
$859$	−1.76776	+	1.35645i	−0.0603152	+	0.0462815i	−0.638479	−	0.769639i	$-0.720436\pi$
$859$	−1.76776	+	1.35645i	−0.0603152	+	0.0462815i	0.578164	+	0.815921i	$0.303769\pi$
$860$	22.6835	−	4.51203i	0.773501	−	0.153859i
$861$	−5.27685	+	30.6385i	−0.179835	+	1.04416i
$862$	7.05479	−	35.4668i	0.240287	−	1.20801i
$863$	−3.50463	+	0.939061i	−0.119299	+	0.0319660i	−0.317974	−	0.948099i	$-0.603003\pi$
$863$	−3.50463	+	0.939061i	−0.119299	+	0.0319660i	0.198676	+	0.980065i	$0.436336\pi$
$864$	−6.55959	−	3.23483i	−0.223162	−	0.110051i
$865$	−3.04671	−	2.33782i	−0.103591	−	0.0794884i
$866$	2.16804	−	3.75516i	0.0736730	−	0.127605i
$867$	−3.06314	+	16.7218i	−0.104030	+	0.567901i
$868$	−8.12137	+	11.1690i	−0.275657	+	0.379101i
$869$	31.3004	+	75.5659i	1.06179	+	2.56340i
$870$	0.247697	+	3.77913i	0.00839773	+	0.128125i
$871$	12.2549	−	45.7360i	0.415242	−	1.54971i
$872$	9.51556	+	28.0319i	0.322238	+	0.949281i
$873$	−3.10067	−	6.28753i	−0.104942	−	0.212801i
$874$	1.53692	+	7.72662i	0.0519871	+	0.261357i
$875$	26.4828	+	14.3923i	0.895282	+	0.486547i
$876$	−1.31161	+	3.16650i	−0.0443150	+	0.106986i
$877$	−34.1500	−	11.5924i	−1.15316	−	0.391446i	−0.321600	−	0.946876i	$-0.604220\pi$
$877$	−34.1500	−	11.5924i	−1.15316	−	0.391446i	−0.831564	+	0.555430i	$0.812554\pi$
$878$	5.28278	−	80.5997i	0.178285	−	2.72011i
$879$	−14.6647	+	4.97800i	−0.494629	+	0.167904i
$880$	3.01578	+	11.2550i	0.101662	+	0.379407i
$881$	9.29781	−	6.21260i	0.313251	−	0.209308i	−0.388999	−	0.921238i	$-0.627179\pi$
$881$	9.29781	−	6.21260i	0.313251	−	0.209308i	0.702250	+	0.711931i	$0.252179\pi$
$882$	9.96875	+	11.6902i	0.335665	+	0.393630i
$883$		−	0.949202i		−	0.0319432i	−0.999872	−	0.0159716i	$-0.994916\pi$
$883$		−	0.949202i		−	0.0319432i	0.999872	−	0.0159716i	$-0.00508413\pi$
$884$	58.3181	−	45.4562i	1.96145	−	1.52886i
$885$	13.2711	−	7.66207i	0.446103	−	0.257558i
$886$	−48.2362	+	62.8626i	−1.62053	+	2.11191i
$887$	6.56890	−	0.430549i	0.220562	−	0.0144564i	0.0452786	−	0.998974i	$-0.485582\pi$
$887$	6.56890	−	0.430549i	0.220562	−	0.0144564i	0.175284	+	0.984518i	$0.443916\pi$
$888$	−6.05652	−	6.05652i	−0.203243	−	0.203243i
$889$	−5.67625	+	18.2556i	−0.190375	+	0.612272i
$890$	−24.1265	−	16.1208i	−0.808722	−	0.540371i
$891$	1.53774	−	4.53003i	0.0515162	−	0.151762i
$892$	−23.9230	+	3.14953i	−0.801002	+	0.105454i
$893$	−18.1184	+	2.38533i	−0.606309	+	0.0798221i
$894$	13.4965	−	39.7595i	0.451392	−	1.32976i
$895$	−3.45597	−	2.30921i	−0.115520	−	0.0771883i
$896$	25.5561	−	23.6055i	0.853769	−	0.788604i
$897$	5.73292	+	5.73292i	0.191417	+	0.191417i
$898$	−20.0479	+	1.31401i	−0.669009	+	0.0438491i
$899$	1.35700	−	1.76847i	0.0452584	−	0.0589818i
$900$	−7.17964	+	4.14517i	−0.239321	+	0.138172i
$901$	−5.20164	+	9.16947i	−0.173292	+	0.305479i
$902$			123.379i			4.10807i
$903$	−10.4290	+	10.9814i	−0.347057	+	0.365439i
$904$	−25.5318	+	17.0598i	−0.849176	+	0.567401i
$905$	0.589722	+	2.20087i	0.0196030	+	0.0731595i
$906$	−19.3344	+	6.56314i	−0.642342	+	0.218046i
$907$	−1.42892	+	21.8011i	−0.0474465	+	0.723894i	0.906178	+	0.422896i	$0.138986\pi$
$907$	−1.42892	+	21.8011i	−0.0474465	+	0.723894i	−0.953625	+	0.300998i	$0.902680\pi$
$908$	23.2275	+	7.88467i	0.770831	+	0.261662i
$909$	2.19870	−	5.30813i	0.0729263	−	0.176060i
$910$	1.36738	+	53.0014i	0.0453281	+	1.75698i
$911$	−3.62815	−	18.2399i	−0.120206	−	0.604316i	−0.993184	−	0.116557i	$-0.962814\pi$
$911$	−3.62815	−	18.2399i	−0.120206	−	0.604316i	0.872978	−	0.487759i	$-0.162186\pi$
$912$	2.11685	+	4.29254i	0.0700959	+	0.142140i
$913$	9.91010	+	29.1942i	0.327976	+	0.966187i
$914$	−17.9868	+	67.1276i	−0.594950	+	2.22038i
$915$	−1.15089	−	17.5593i	−0.0380474	−	0.580491i
$916$	16.1015	+	38.8724i	0.532008	+	1.28438i
$917$	20.9037	+	15.1998i	0.690302	+	0.501942i
$918$	8.86180	−	1.83273i	0.292483	−	0.0604891i
$919$	23.0071	−	39.8495i	0.758935	−	1.31451i	−0.184459	−	0.982840i	$-0.559053\pi$
$919$	23.0071	−	39.8495i	0.758935	−	1.31451i	0.943394	−	0.331674i	$-0.107613\pi$
$920$	2.59887	+	1.99419i	0.0856823	+	0.0657463i
$921$	19.1996	+	9.46818i	0.632647	+	0.311987i
$922$	5.31101	−	1.42308i	0.174909	−	0.0468666i
$923$	−7.68934	+	38.6569i	−0.253098	+	1.27241i
$924$	27.4050	+	22.8104i	0.901557	+	0.750407i
$925$	13.7856	−	2.74213i	0.453268	−	0.0901605i
$926$	−10.5698	+	8.11053i	−0.347347	+	0.266529i
$927$	−1.19767	−	9.09719i	−0.0393365	−	0.298791i
$928$	−6.61564	+	5.80176i	−0.217169	+	0.190452i
$929$	6.02117	−	2.96931i	0.197548	−	0.0974200i	−0.340824	−	0.940127i	$-0.610706\pi$
$929$	6.02117	−	2.96931i	0.197548	−	0.0974200i	0.538372	+	0.842707i	$0.319039\pi$
$930$	−5.72040	−	1.13786i	−0.187579	−	0.0373119i
$931$	−1.01726	−	19.7022i	−0.0333395	−	0.645712i
$932$	−31.9172	−	47.7674i	−1.04548	−	1.56467i
$933$	1.16698	−	8.86409i	0.0382052	−	0.290197i
$934$	41.3561	+	71.6308i	1.35321	+	2.34383i
$935$	−22.5742	−	17.0512i	−0.738256	−	0.557635i
$936$	−9.88668	−	5.70808i	−0.323156	−	0.186574i
$937$	−13.2087	+	5.47122i	−0.431509	+	0.178737i	−0.587856	−	0.808965i	$-0.700028\pi$
$937$	−13.2087	+	5.47122i	−0.431509	+	0.178737i	0.156348	+	0.987702i	$0.450028\pi$
$938$	20.0956	+	38.2314i	0.656146	+	1.24830i
$939$	9.07532	−	9.07532i	0.296162	−	0.296162i
$940$	−17.2743	+	19.6976i	−0.563426	+	0.642464i
$941$	17.2531	+	1.13082i	0.562433	+	0.0368638i	0.343969	−	0.938981i	$-0.388229\pi$
$941$	17.2531	+	1.13082i	0.562433	+	0.0368638i	0.218465	+	0.975845i	$0.429895\pi$
$942$	−2.33780	−	2.66574i	−0.0761695	−	0.0868547i
$943$	−9.11050	−	11.8730i	−0.296679	−	0.386639i
$944$	16.7630	+	6.94346i	0.545589	+	0.225990i
$945$	−1.59003	+	3.44553i	−0.0517236	+	0.112083i
$946$	−33.3903	+	49.9722i	−1.08561	+	1.62473i
$947$	8.97310	+	7.86920i	0.291587	+	0.255715i	0.792624	−	0.609711i	$-0.208715\pi$
$947$	8.97310	+	7.86920i	0.291587	+	0.255715i	−0.501037	+	0.865426i	$0.667048\pi$
$948$	46.5233	+	12.4659i	1.51101	+	0.404873i
$949$	3.42555	−	6.94633i	0.111198	−	0.225487i
$950$	18.0479	+	2.37605i	0.585551	+	0.0770893i
$951$	−10.2646			−0.332853
$952$	−3.17404	+	19.3037i	−0.102871	+	0.625635i
$953$	8.74798			0.283375			0.141688	−	0.989911i	$-0.454747\pi$
$953$	8.74798			0.283375			0.141688	+	0.989911i	$0.454747\pi$
$954$	5.56370	+	0.732476i	0.180132	+	0.0237148i
$955$	9.41692	−	19.0956i	0.304725	−	0.617920i
$956$	41.9637	+	11.2442i	1.35720	+	0.363662i
$957$	−4.32722	−	3.79487i	−0.139879	−	0.122671i
$958$	18.0998	−	27.0882i	0.584776	−	0.875180i
$959$	−6.55389	+	4.62803i	−0.211636	+	0.149447i
$960$	16.7702	+	6.94645i	0.541256	+	0.224196i
$961$	−16.7818	−	21.8704i	−0.541348	−	0.705498i
$962$	43.9993	+	50.1716i	1.41859	+	1.61760i
$963$	7.16564	+	0.469661i	0.230910	+	0.0151346i
$964$	27.0007	−	30.7884i	0.869633	−	0.991626i
$965$	3.47773	−	3.47773i	0.111952	−	0.111952i
$966$	−7.38974	−	0.293206i	−0.237761	−	0.00943376i
$967$	41.1194	−	17.0322i	1.32231	−	0.547719i	0.393858	−	0.919171i	$-0.371140\pi$
$967$	41.1194	−	17.0322i	1.32231	−	0.547719i	0.928452	+	0.371453i	$0.121140\pi$
$968$	18.4594	+	10.6575i	0.593308	+	0.342547i
$969$	−10.4606	−	5.06031i	−0.336044	−	0.162561i
$970$	11.0342	+	19.1118i	0.354287	+	0.613643i
$971$	6.60184	−	50.1459i	0.211863	−	1.60926i	−0.473321	−	0.880890i	$-0.656945\pi$
$971$	6.60184	−	50.1459i	0.211863	−	1.60926i	0.685184	−	0.728370i	$-0.259722\pi$
$972$	−1.56509	−	2.34232i	−0.0502002	−	0.0751299i
$973$	−38.9364	+	31.5052i	−1.24824	+	1.01001i
$974$	33.1206	+	6.58810i	1.06125	+	0.211096i
$975$	16.8021	−	8.28589i	0.538099	−	0.265361i
$976$	15.6647	−	13.7376i	0.501416	−	0.439730i
$977$	−7.58745	−	57.6324i	−0.242744	−	1.84382i	−0.486121	−	0.873892i	$-0.661588\pi$
$977$	−7.58745	−	57.6324i	−0.242744	−	1.84382i	0.243377	−	0.969932i	$-0.421745\pi$
$978$	21.4347	−	16.4474i	0.685406	−	0.525930i
$979$	43.2497	−	8.60289i	1.38227	−	0.274950i
$980$	−19.7200	−	20.2745i	−0.629933	−	0.647646i
$981$	3.22042	−	16.1901i	0.102820	−	0.516911i
$982$	−57.3235	+	15.3598i	−1.82927	+	0.490150i
$983$	42.4104	+	20.9145i	1.35268	+	0.667068i	0.966813	−	0.255486i	$-0.0822355\pi$
$983$	42.4104	+	20.9145i	1.35268	+	0.667068i	0.385868	+	0.922554i	$0.373902\pi$
$984$	16.7183	+	12.8284i	0.532959	+	0.408954i
$985$	1.54275	−	2.67213i	0.0491562	−	0.0851411i
$986$	2.04291	−	10.6938i	0.0650596	−	0.340561i
$987$	1.79985	−	17.0609i	0.0572899	−	0.543056i
$988$	19.3417	+	46.6949i	0.615341	+	1.48556i
$989$	−0.476798	−	7.27454i	−0.0151613	−	0.231317i
$990$	−3.89764	+	14.5462i	−0.123875	+	0.462308i
$991$	−2.33668	−	6.88363i	−0.0742270	−	0.218666i	0.903484	−	0.428623i	$-0.141001\pi$
$991$	−2.33668	−	6.88363i	−0.0742270	−	0.218666i	−0.977711	+	0.209957i	$0.932668\pi$
$992$	−5.99353	−	12.1537i	−0.190295	−	0.385879i
$993$	2.75603	+	13.8555i	0.0874599	+	0.439691i
$994$	−18.7735	−	30.6621i	−0.595458	−	0.972544i
$995$	−9.85763	+	23.7984i	−0.312508	+	0.754461i
$996$	17.1915	+	5.83572i	0.544733	+	0.184912i
$997$	2.60729	−	39.7795i	0.0825736	−	1.25983i	−0.732619	−	0.680639i	$-0.761702\pi$
$997$	2.60729	−	39.7795i	0.0825736	−	1.25983i	0.815192	−	0.579190i	$-0.196631\pi$
$998$	−12.2933	+	4.17301i	−0.389138	+	0.132094i
$999$	1.23616	+	4.61342i	0.0391104	+	0.145962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.250.21	yes	384
7.3	odd	6	inner	357.2.bl.a.199.4	yes	384
17.10	odd	16	inner	357.2.bl.a.61.4	yes	384
119.10	even	48	inner	357.2.bl.a.10.21	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.21	✓	384	119.10	even	48	inner
357.2.bl.a.61.4	yes	384	17.10	odd	16	inner
357.2.bl.a.199.4	yes	384	7.3	odd	6	inner
357.2.bl.a.250.21	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+(2.17601 + 0.286477i) q^{2} +(-0.442289 + 0.896873i) q^{3} +(2.72109 + 0.729115i) q^{4} +(1.07834 + 0.945678i) q^{5} +(-1.21936 + 1.82490i) q^{6} +(0.241071 + 2.63475i) q^{7} +(1.65682 + 0.686276i) q^{8} +(-0.608761 - 0.793353i) q^{9} +(2.07556 + 2.36672i) q^{10} +(-4.77367 - 0.312883i) q^{11} +(-1.85743 + 2.11800i) q^{12} +(4.50138 - 4.50138i) q^{13} +(-0.230220 + 5.80229i) q^{14} +(-1.32509 + 0.548870i) q^{15} +(-1.47069 - 0.849103i) q^{16} +(4.08363 - 0.569174i) q^{17} +(-1.09739 - 1.90074i) q^{18} +(-0.367867 + 2.79423i) q^{19} +(2.24475 + 3.35951i) q^{20} +(-2.46965 - 0.949108i) q^{21} +(-10.2979 - 2.04838i) q^{22} +(1.14225 - 0.563294i) q^{23} +(-1.34829 + 1.18242i) q^{24} +(-0.384123 - 2.91770i) q^{25} +(11.0846 - 8.50551i) q^{26} +(0.980785 - 0.195090i) q^{27} +(-1.26505 + 7.34516i) q^{28} +(0.234713 - 1.17998i) q^{29} +(-3.04065 + 0.814738i) q^{30} +(1.66173 + 0.819477i) q^{31} +(-5.80246 - 4.45239i) q^{32} +(2.39196 - 4.14299i) q^{33} +(9.04907 - 0.0686616i) q^{34} +(-2.23166 + 3.06912i) q^{35} +(-1.07805 - 2.60265i) q^{36} +(0.312376 + 4.76594i) q^{37} +(-1.60097 + 5.97489i) q^{38} +(2.04626 + 6.02808i) q^{39} +(1.13761 + 2.30685i) q^{40} +(-2.29246 - 11.5250i) q^{41} +(-5.10209 - 2.77277i) q^{42} +(2.19051 - 5.28837i) q^{43} +(-12.7615 - 4.33194i) q^{44} +(0.0938055 - 1.43120i) q^{45} +(2.64691 - 0.898506i) q^{46} +(1.67824 + 6.26327i) q^{47} +(1.41201 - 0.943472i) q^{48} +(-6.88377 + 1.27032i) q^{49} -6.45899i q^{50} +(-1.29567 + 3.91424i) q^{51} +(15.5307 - 8.96666i) q^{52} +(-1.55650 + 2.02848i) q^{53} +(2.19009 - 0.143546i) q^{54} +(-4.85174 - 4.85174i) q^{55} +(-1.40875 + 4.53073i) q^{56} +(-2.34337 - 1.56579i) q^{57} +(0.848774 - 2.50041i) q^{58} +(-10.5929 + 1.39458i) q^{59} +(-4.00588 + 0.527384i) q^{60} +(-3.94372 + 11.6178i) q^{61} +(3.38119 + 2.25924i) q^{62} +(1.94353 - 1.79519i) q^{63} +(-8.94908 - 8.94908i) q^{64} +(9.11087 - 0.597158i) q^{65} +(6.39179 - 8.32994i) q^{66} +(6.44146 - 3.71898i) q^{67} +(11.5269 + 1.42866i) q^{68} +1.27359i q^{69} +(-5.73535 + 6.03912i) q^{70} +(-5.14800 + 3.43979i) q^{71} +(-0.464147 - 1.73222i) q^{72} +(1.15208 - 0.391078i) q^{73} +(-0.685599 + 10.4602i) q^{74} +(2.78670 + 0.945958i) q^{75} +(-3.03832 + 7.33515i) q^{76} +(-0.326429 - 12.6528i) q^{77} +(2.72577 + 13.7034i) q^{78} +(-7.56194 - 15.3341i) q^{79} +(-0.782923 - 2.30642i) q^{80} +(-0.258819 + 0.965926i) q^{81} +(-1.68677 - 25.7352i) q^{82} +(-2.46624 - 5.95403i) q^{83} +(-6.02815 - 4.38327i) q^{84} +(4.94179 + 3.24804i) q^{85} +(6.28158 - 10.8800i) q^{86} +(0.954481 + 0.732399i) q^{87} +(-7.69436 - 3.79444i) q^{88} +(-8.90368 + 2.38573i) q^{89} +(0.614126 - 3.08742i) q^{90} +(12.9452 + 10.7748i) q^{91} +(3.51887 - 0.699947i) q^{92} +(-1.46993 + 1.12792i) q^{93} +(1.85758 + 14.1097i) q^{94} +(-3.03913 + 2.66524i) q^{95} +(6.55959 - 3.23483i) q^{96} +(6.87580 + 1.36768i) q^{97} +(-15.3431 + 0.792195i) q^{98} +(2.65780 + 3.97768i) 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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