LMFDB - Embedded newform 350.2.x.a.3.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,2,Mod(3,350)] 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("350.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.x (of order $60$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$20$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	350.3
Dual form			350.2.x.a.117.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.544639 + 0.838671i) q^{2} +(-1.15652 + 3.01283i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.77963 - 1.35386i) q^{5} +(-1.89689 - 2.61084i) q^{6} +(-0.00275235 + 2.64575i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-5.51019 - 4.96140i) q^{9} +(2.10469 - 0.755156i) q^{10} +(0.696124 + 0.773125i) q^{11} +(3.22276 - 0.168898i) q^{12} +(-3.97493 - 2.02533i) q^{13} +(-2.21741 - 1.44329i) q^{14} +(6.13712 - 3.79595i) q^{15} +(-0.669131 + 0.743145i) q^{16} +(1.70623 - 2.10702i) q^{17} +(7.16204 - 1.91906i) q^{18} +(-2.97009 - 1.32237i) q^{19} +(-0.512972 + 2.17643i) q^{20} +(-7.96802 - 3.06815i) q^{21} +(-1.02753 + 0.162745i) q^{22} +(4.00771 + 2.60264i) q^{23} +(-1.61359 + 2.79482i) q^{24} +(1.33414 + 4.81872i) q^{25} +(3.86349 - 2.23059i) q^{26} +(12.6942 - 6.46801i) q^{27} +(2.41813 - 1.07361i) q^{28} +(2.96953 - 4.08721i) q^{29} +(-0.158959 + 7.21444i) q^{30} +(-5.23139 + 0.549842i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-3.13438 + 1.20317i) q^{33} +(0.837815 + 2.57853i) q^{34} +(3.58687 - 4.70472i) q^{35} +(-2.29127 + 7.05179i) q^{36} +(0.133100 + 2.53970i) q^{37} +(2.72666 - 1.77072i) q^{38} +(10.6991 - 9.63348i) q^{39} +(-1.54593 - 1.61558i) q^{40} +(1.71718 - 0.557946i) q^{41} +(6.91286 - 5.01151i) q^{42} +(-4.92704 - 4.92704i) q^{43} +(0.423145 - 0.950399i) q^{44} +(3.08905 + 16.2894i) q^{45} +(-4.36551 + 1.94365i) q^{46} +(-9.14075 + 7.40204i) q^{47} +(-1.46511 - 2.87544i) q^{48} +(-6.99998 - 0.0145640i) q^{49} +(-4.76794 - 1.50556i) q^{50} +(4.37481 + 7.57739i) q^{51} +(-0.233480 + 4.45506i) q^{52} +(-6.25807 - 2.40225i) q^{53} +(-1.48922 + 14.1690i) q^{54} +(-0.192140 - 2.31833i) q^{55} +(-0.416605 + 2.61275i) q^{56} +(7.41905 - 7.41905i) q^{57} +(1.81050 + 4.71651i) q^{58} +(-13.2080 - 2.80746i) q^{59} +(-5.96397 - 4.06258i) q^{60} +(-0.578601 - 2.72210i) q^{61} +(2.38808 - 4.68688i) q^{62} +(13.1418 - 14.5649i) q^{63} +(0.951057 + 0.309017i) q^{64} +(4.33188 + 8.98582i) q^{65} +(0.698037 - 3.28400i) q^{66} +(-4.15021 - 3.36077i) q^{67} +(-2.61884 - 0.701717i) q^{68} +(-12.4763 + 9.06456i) q^{69} +(1.99216 + 5.57057i) q^{70} +(6.39697 + 4.64767i) q^{71} +(-4.66622 - 5.76230i) q^{72} +(-16.7907 - 0.879961i) q^{73} +(-2.20246 - 1.27159i) q^{74} +(-16.0610 - 1.55341i) q^{75} +3.25117i q^{76} +(-2.04741 + 1.83964i) q^{77} +(2.25219 + 14.2198i) q^{78} +(-11.8413 - 1.24458i) q^{79} +(2.19691 - 0.416612i) q^{80} +(2.48084 + 23.6036i) q^{81} +(-0.467311 + 1.74403i) q^{82} +(0.547617 - 3.45752i) q^{83} +(0.437991 + 8.52708i) q^{84} +(-5.88906 + 1.43971i) q^{85} +(6.81562 - 1.44871i) q^{86} +(8.87976 + 13.6736i) q^{87} +(0.566611 + 0.872504i) q^{88} +(11.4050 - 2.42420i) q^{89} +(-15.3439 - 6.28118i) q^{90} +(5.36946 - 10.5111i) q^{91} +(0.747545 - 4.71981i) q^{92} +(4.39362 - 16.3972i) q^{93} +(-1.22946 - 11.6975i) q^{94} +(3.49535 + 6.37441i) q^{95} +(3.20950 + 0.337332i) q^{96} +(0.878465 + 5.54641i) q^{97} +(3.82468 - 5.86275i) q^{98} -7.71381i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37}+ \cdots - 40 q^{98}+O(q^{100}) $ 320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.544639	+	0.838671i	−0.385118	+	0.593030i
$2$	−0.544639	+	0.838671i	−0.385118	+	0.593030i
$3$	−1.15652	+	3.01283i	−0.667716	+	1.73946i	0.00546846	+	0.999985i	$0.498259\pi$
$3$	−1.15652	+	3.01283i	−0.667716	+	1.73946i	−0.673184	+	0.739475i	$0.735074\pi$
$4$	−0.406737	−	0.913545i	−0.203368	−	0.456773i
$5$	−1.77963	−	1.35386i	−0.795873	−	0.605464i
$5$	−1.77963	−	1.35386i	−0.795873	−	0.605464i
$6$	−1.89689	−	2.61084i	−0.774402	−	1.06587i
$7$	−0.00275235	+	2.64575i	−0.00104029	+	0.999999i
$7$	−0.00275235	+	2.64575i	−0.00104029	+	0.999999i
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	−5.51019	−	4.96140i	−1.83673	−	1.65380i
$10$	2.10469	−	0.755156i	0.665563	−	0.238801i
$11$	0.696124	+	0.773125i	0.209889	+	0.233106i	0.838893	−	0.544297i	$-0.183203\pi$
$11$	0.696124	+	0.773125i	0.209889	+	0.233106i	−0.629003	+	0.777403i	$0.716537\pi$
$12$	3.22276	−	0.168898i	0.930330	−	0.0487565i
$13$	−3.97493	−	2.02533i	−1.10245	−	0.561725i	−0.194540	−	0.980895i	$-0.562321\pi$
$13$	−3.97493	−	2.02533i	−1.10245	−	0.561725i	−0.907908	+	0.419169i	$0.862321\pi$
$14$	−2.21741	−	1.44329i	−0.592629	−	0.385735i
$15$	6.13712	−	3.79595i	1.58460	−	0.980111i
$16$	−0.669131	+	0.743145i	−0.167283	+	0.185786i
$17$	1.70623	−	2.10702i	0.413822	−	0.511027i	−0.527030	−	0.849847i	$-0.676694\pi$
$17$	1.70623	−	2.10702i	0.413822	−	0.511027i	0.940851	+	0.338820i	$0.110028\pi$
$18$	7.16204	−	1.91906i	1.68811	−	0.452328i
$19$	−2.97009	−	1.32237i	−0.681386	−	0.303373i	0.0367005	−	0.999326i	$-0.488315\pi$
$19$	−2.97009	−	1.32237i	−0.681386	−	0.303373i	−0.718087	+	0.695954i	$0.754982\pi$
$20$	−0.512972	+	2.17643i	−0.114704	+	0.486665i
$21$	−7.96802	−	3.06815i	−1.73876	−	0.669525i
$22$	−1.02753	+	0.162745i	−0.219071	+	0.0346974i
$23$	4.00771	+	2.60264i	0.835665	+	0.542687i	0.890066	−	0.455832i	$-0.150658\pi$
$23$	4.00771	+	2.60264i	0.835665	+	0.542687i	−0.0544007	+	0.998519i	$0.517325\pi$
$24$	−1.61359	+	2.79482i	−0.329373	+	0.570490i
$25$	1.33414	+	4.81872i	0.266827	+	0.963744i
$26$	3.86349	−	2.23059i	0.757692	−	0.437454i
$27$	12.6942	−	6.46801i	2.44300	−	1.24477i
$28$	2.41813	−	1.07361i	0.456984	−	0.202893i
$29$	2.96953	−	4.08721i	0.551428	−	0.758976i	−0.438777	−	0.898596i	$-0.644588\pi$
$29$	2.96953	−	4.08721i	0.551428	−	0.758976i	0.990205	+	0.139620i	$0.0445881\pi$
$30$	−0.158959	+	7.21444i	−0.0290219	+	1.31717i
$31$	−5.23139	+	0.549842i	−0.939586	+	0.0987545i	−0.561924	−	0.827189i	$-0.689939\pi$
$31$	−5.23139	+	0.549842i	−0.939586	+	0.0987545i	−0.377662	+	0.925943i	$0.623272\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−3.13438	+	1.20317i	−0.545625	+	0.209446i
$34$	0.837815	+	2.57853i	0.143684	+	0.442214i
$35$	3.58687	−	4.70472i	0.606291	−	0.795243i
$36$	−2.29127	+	7.05179i	−0.381878	+	1.17530i
$37$	0.133100	+	2.53970i	0.0218815	+	0.417524i	0.987506	+	0.157582i	$0.0503699\pi$
$37$	0.133100	+	2.53970i	0.0218815	+	0.417524i	−0.965624	+	0.259941i	$0.916297\pi$
$38$	2.72666	−	1.77072i	0.442323	−	0.287248i
$39$	10.6991	−	9.63348i	1.71322	−	1.54259i
$40$	−1.54593	−	1.61558i	−0.244432	−	0.255446i
$41$	1.71718	−	0.557946i	0.268178	−	0.0871365i	−0.171841	−	0.985125i	$-0.554972\pi$
$41$	1.71718	−	0.557946i	0.268178	−	0.0871365i	0.440019	+	0.897988i	$0.354972\pi$
$42$	6.91286	−	5.01151i	1.06668	−	0.773292i
$43$	−4.92704	−	4.92704i	−0.751367	−	0.751367i	0.223368	−	0.974734i	$-0.428295\pi$
$43$	−4.92704	−	4.92704i	−0.751367	−	0.751367i	−0.974734	+	0.223368i	$0.928295\pi$
$44$	0.423145	−	0.950399i	0.0637915	−	0.143278i
$45$	3.08905	+	16.2894i	0.460488	+	2.42829i
$46$	−4.36551	+	1.94365i	−0.643659	+	0.286576i
$47$	−9.14075	+	7.40204i	−1.33332	+	1.07970i	−0.343227	+	0.939252i	$0.611520\pi$
$47$	−9.14075	+	7.40204i	−1.33332	+	1.07970i	−0.990088	+	0.140445i	$0.955147\pi$
$48$	−1.46511	−	2.87544i	−0.211470	−	0.415034i
$49$	−6.99998	−	0.0145640i	−0.999998	−	0.00208058i
$50$	−4.76794	−	1.50556i	−0.674289	−	0.212919i
$51$	4.37481	+	7.57739i	0.612596	+	1.06105i
$52$	−0.233480	+	4.45506i	−0.0323778	+	0.617805i
$53$	−6.25807	−	2.40225i	−0.859612	−	0.329974i	−0.111676	−	0.993745i	$-0.535622\pi$
$53$	−6.25807	−	2.40225i	−0.859612	−	0.329974i	−0.747936	+	0.663771i	$0.768955\pi$
$54$	−1.48922	+	14.1690i	−0.202657	+	1.92815i
$55$	−0.192140	−	2.31833i	−0.0259082	−	0.312603i
$56$	−0.416605	+	2.61275i	−0.0556712	+	0.349143i
$57$	7.41905	−	7.41905i	0.982677	−	0.982677i
$58$	1.81050	+	4.71651i	0.237730	+	0.619309i
$59$	−13.2080	−	2.80746i	−1.71954	−	0.365500i	−0.760625	−	0.649192i	$-0.775107\pi$
$59$	−13.2080	−	2.80746i	−1.71954	−	0.365500i	−0.958915	+	0.283692i	$0.908441\pi$
$60$	−5.96397	−	4.06258i	−0.769945	−	0.524477i
$61$	−0.578601	−	2.72210i	−0.0740822	−	0.348530i	0.925458	−	0.378850i	$-0.123680\pi$
$61$	−0.578601	−	2.72210i	−0.0740822	−	0.348530i	−0.999540	+	0.0303207i	$0.990347\pi$
$62$	2.38808	−	4.68688i	0.303287	−	0.595234i
$63$	13.1418	−	14.5649i	1.65571	−	1.83501i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	4.33188	+	8.98582i	0.537304	+	1.11455i
$66$	0.698037	−	3.28400i	0.0859224	−	0.404233i
$67$	−4.15021	−	3.36077i	−0.507029	−	0.410584i	0.341380	−	0.939925i	$-0.389106\pi$
$67$	−4.15021	−	3.36077i	−0.507029	−	0.410584i	−0.848409	+	0.529342i	$0.822439\pi$
$68$	−2.61884	−	0.701717i	−0.317581	−	0.0850957i
$69$	−12.4763	+	9.06456i	−1.50197	+	1.09124i
$70$	1.99216	+	5.57057i	0.238109	+	0.665811i
$71$	6.39697	+	4.64767i	0.759181	+	0.551577i	0.898659	−	0.438648i	$-0.144542\pi$
$71$	6.39697	+	4.64767i	0.759181	+	0.551577i	−0.139478	+	0.990225i	$0.544542\pi$
$72$	−4.66622	−	5.76230i	−0.549919	−	0.679093i
$73$	−16.7907	−	0.879961i	−1.96520	−	0.102992i	−0.973259	−	0.229710i	$-0.926222\pi$
$73$	−16.7907	−	0.879961i	−1.96520	−	0.102992i	−0.991939	+	0.126719i	$0.959555\pi$
$74$	−2.20246	−	1.27159i	−0.256031	−	0.147820i
$75$	−16.0610	−	1.55341i	−1.85456	−	0.179372i
$76$			3.25117i			0.372935i
$77$	−2.04741	+	1.83964i	−0.233324	+	0.209647i
$78$	2.25219	+	14.2198i	0.255010	+	1.61007i
$79$	−11.8413	−	1.24458i	−1.33226	−	0.140026i	−0.588511	−	0.808490i	$-0.700285\pi$
$79$	−11.8413	−	1.24458i	−1.33226	−	0.140026i	−0.743745	+	0.668464i	$0.766952\pi$
$80$	2.19691	−	0.416612i	0.245623	−	0.0465786i
$81$	2.48084	+	23.6036i	0.275649	+	2.62262i
$82$	−0.467311	+	1.74403i	−0.0516058	+	0.192596i
$83$	0.547617	−	3.45752i	0.0601088	−	0.379512i	−0.939235	−	0.343276i	$-0.888463\pi$
$83$	0.547617	−	3.45752i	0.0601088	−	0.379512i	0.999343	−	0.0362356i	$-0.0115367\pi$
$84$	0.437991	+	8.52708i	0.0477887	+	0.930380i
$85$	−5.88906	+	1.43971i	−0.638758	+	0.156159i
$86$	6.81562	−	1.44871i	0.734948	−	0.156218i
$87$	8.87976	+	13.6736i	0.952011	+	1.46597i
$88$	0.566611	+	0.872504i	0.0604009	+	0.0930092i
$89$	11.4050	−	2.42420i	1.20893	−	0.256965i	0.441002	−	0.897506i	$-0.354623\pi$
$89$	11.4050	−	2.42420i	1.20893	−	0.256965i	0.767924	+	0.640541i	$0.221290\pi$
$90$	−15.3439	−	6.28118i	−1.61739	−	0.662094i
$91$	5.36946	−	10.5111i	0.562872	−	1.10186i
$92$	0.747545	−	4.71981i	0.0779369	−	0.492074i
$93$	4.39362	−	16.3972i	0.455597	−	1.70031i
$94$	−1.22946	−	11.6975i	−0.126809	−	1.20651i
$95$	3.49535	+	6.37441i	0.358616	+	0.654001i
$96$	3.20950	+	0.337332i	0.327568	+	0.0344288i
$97$	0.878465	+	5.54641i	0.0891946	+	0.563153i	0.991298	+	0.131634i	$0.0420222\pi$
$97$	0.878465	+	5.54641i	0.0891946	+	0.563153i	−0.902104	+	0.431519i	$0.857978\pi$
$98$	3.82468	−	5.86275i	0.386351	−	0.592227i
$99$		−	7.71381i		−	0.775268i
$100$	3.85948	−	3.17875i	0.385948	−	0.317875i
$101$	16.2110	+	9.35943i	1.61305	+	0.931298i	0.988657	+	0.150191i	$0.0479890\pi$
$101$	16.2110	+	9.35943i	1.61305	+	0.931298i	0.624398	+	0.781106i	$0.285344\pi$
$102$	−8.73763	−	0.457920i	−0.865154	−	0.0453408i
$103$	10.2302	+	12.6332i	1.00801	+	1.24479i	0.969388	+	0.245534i	$0.0789635\pi$
$103$	10.2302	+	12.6332i	1.00801	+	1.24479i	0.0386219	+	0.999254i	$0.487703\pi$
$104$	−3.60916	−	2.62221i	−0.353908	−	0.257129i
$105$	10.0263	+	16.2477i	0.978462	+	1.58562i
$106$	5.42308	−	3.94010i	0.526736	−	0.382696i
$107$	3.51372	+	0.941500i	0.339685	+	0.0910182i	0.424629	−	0.905367i	$-0.360405\pi$
$107$	3.51372	+	0.941500i	0.339685	+	0.0910182i	−0.0849443	+	0.996386i	$0.527071\pi$
$108$	−11.0720	−	8.96594i	−1.06540	−	0.862748i
$109$	−0.830506	+	3.90722i	−0.0795481	+	0.374244i	−0.999856	−	0.0169497i	$-0.994604\pi$
$109$	−0.830506	+	3.90722i	−0.0795481	+	0.374244i	0.920308	+	0.391194i	$0.127938\pi$
$110$	2.04896	+	1.10151i	0.195361	+	0.105025i
$111$	−7.80562	−	2.53620i	−0.740876	−	0.240725i
$112$	−1.96433	−	1.77240i	−0.185612	−	0.167476i
$113$	−2.52013	+	4.94603i	−0.237074	+	0.465284i	−0.978636	−	0.205601i	$-0.934085\pi$
$113$	−2.52013	+	4.94603i	−0.237074	+	0.465284i	0.741562	+	0.670884i	$0.234085\pi$
$114$	2.18143	+	10.2628i	0.204310	+	0.961203i
$115$	−3.60862	−	10.0576i	−0.336506	−	0.937875i
$116$	−4.94167	−	1.05038i	−0.458823	−	0.0975258i
$117$	11.8542	+	30.8812i	1.09592	+	2.85497i
$118$	9.54814	−	9.54814i	0.878978	−	0.878978i
$119$	5.56995	+	4.52006i	0.510596	+	0.414353i
$120$	6.65538	−	2.78916i	0.607550	−	0.254615i
$121$	1.03668	−	9.86336i	0.0942437	−	0.896669i
$122$	2.59808	+	0.997308i	0.235219	+	0.0902920i
$123$	−0.304953	+	5.81885i	−0.0274967	+	0.524668i
$124$	2.63010	+	4.55547i	0.236190	+	0.409094i
$125$	4.14960	−	10.3818i	0.371152	−	0.928572i
$126$	5.05765	+	18.9543i	0.450571	+	1.68858i
$127$	4.00141	+	7.85320i	0.355067	+	0.696859i	0.997588	−	0.0694091i	$-0.0221114\pi$
$127$	4.00141	+	7.85320i	0.355067	+	0.696859i	−0.642521	+	0.766268i	$0.722111\pi$
$128$	−0.777146	+	0.629320i	−0.0686906	+	0.0556246i
$129$	20.5426	−	9.14614i	1.80867	−	0.805272i
$130$	−9.89546	−	1.26101i	−0.867889	−	0.110598i
$131$	2.22283	−	4.99256i	0.194210	−	0.436202i	−0.790024	−	0.613076i	$-0.789932\pi$
$131$	2.22283	−	4.99256i	0.194210	−	0.436202i	0.984233	+	0.176874i	$0.0565986\pi$
$132$	2.37402	+	2.37402i	0.206632	+	0.206632i
$133$	3.50684	−	7.85449i	0.304081	−	0.681070i
$134$	5.07895	−	1.65025i	0.438754	−	0.142560i
$135$	−31.3477	−	5.67549i	−2.69798	−	0.488468i
$136$	2.01483	−	1.81416i	0.172771	−	0.155563i
$137$	−12.2908	+	7.98172i	−1.05007	+	0.681925i	−0.949743	−	0.313030i	$-0.898656\pi$
$137$	−12.2908	+	7.98172i	−1.05007	+	0.681925i	−0.100329	+	0.994954i	$0.531989\pi$
$138$	−0.807102	−	15.4004i	−0.0687051	−	1.31097i
$139$	−3.54013	+	10.8954i	−0.300270	+	0.924136i	0.681130	+	0.732163i	$0.261489\pi$
$139$	−3.54013	+	10.8954i	−0.300270	+	0.924136i	−0.981400	+	0.191974i	$0.938511\pi$
$140$	−5.75689	−	1.36319i	−0.486546	−	0.115210i
$141$	−11.7296	−	36.1001i	−0.987815	−	3.04018i
$142$	−7.38191	+	2.83365i	−0.619476	+	0.237795i
$143$	−1.20122	−	4.48300i	−0.100451	−	0.374887i
$144$	7.37408	−	0.775047i	0.614506	−	0.0645872i
$145$	−10.8182	+	3.25338i	−0.898399	+	0.270179i
$146$	9.88284	−	13.6026i	0.817910	−	1.12576i
$147$	8.13949	−	21.0729i	0.671334	−	1.73807i
$148$	2.26599	−	1.15458i	0.186263	−	0.0949060i
$149$	−6.23582	+	3.60025i	−0.510858	+	0.294944i	−0.733186	−	0.680028i	$-0.761968\pi$
$149$	−6.23582	+	3.60025i	−0.510858	+	0.294944i	0.222328	+	0.974972i	$0.428634\pi$
$150$	10.0502	−	12.6238i	0.820597	−	1.03073i
$151$	−2.71980	+	4.71084i	−0.221334	+	0.383362i	−0.955213	−	0.295918i	$-0.904375\pi$
$151$	−2.71980	+	4.71084i	−0.221334	+	0.383362i	0.733879	+	0.679280i	$0.237708\pi$
$152$	−2.72666	−	1.77072i	−0.221162	−	0.143624i
$153$	−19.8554	+	3.14479i	−1.60522	+	0.254241i
$154$	−0.427755	−	2.71904i	−0.0344695	−	0.219107i
$155$	10.0543	+	6.10405i	0.807583	+	0.490289i
$156$	−13.1523	−	5.85579i	−1.05303	−	0.468838i
$157$	−13.1208	+	3.51571i	−1.04715	+	0.280584i	−0.741075	−	0.671422i	$-0.765684\pi$
$157$	−13.1208	+	3.51571i	−1.04715	+	0.280584i	−0.306079	+	0.952006i	$0.599017\pi$
$158$	7.49305	−	9.25314i	0.596115	−	0.736140i
$159$	14.4751	−	16.0763i	1.14795	−	1.27493i
$160$	−0.847125	+	2.06939i	−0.0669711	+	0.163600i
$161$	−6.89696	+	10.5962i	−0.543556	+	0.835100i
$162$	−21.1468	−	10.7748i	−1.66145	−	0.846551i
$163$	10.1717	−	0.533076i	0.796709	−	0.0417537i	0.350363	−	0.936614i	$-0.386058\pi$
$163$	10.1717	−	0.533076i	0.796709	−	0.0417537i	0.446346	+	0.894860i	$0.352725\pi$
$164$	−1.20815	−	1.34178i	−0.0943406	−	0.104776i
$165$	7.20694	+	2.10230i	0.561060	+	0.163664i
$166$	2.60146	+	2.34237i	0.201913	+	0.181803i
$167$	−7.21112	−	1.14213i	−0.558013	−	0.0883806i	−0.128943	−	0.991652i	$-0.541159\pi$
$167$	−7.21112	−	1.14213i	−0.558013	−	0.0883806i	−0.429070	+	0.903271i	$0.641159\pi$
$168$	−7.38995	−	4.27685i	−0.570147	−	0.329966i
$169$	4.05693	+	5.58388i	0.312071	+	0.429529i
$170$	1.99997	−	5.72310i	0.153390	−	0.438942i
$171$	9.80498	+	22.0223i	0.749805	+	1.68409i
$172$	−2.49707	+	6.50508i	−0.190400	+	0.496008i
$173$	1.04287	−	1.60588i	0.0792881	−	0.122093i	−0.796802	−	0.604241i	$-0.793477\pi$
$173$	1.04287	−	1.60588i	0.0792881	−	0.122093i	0.876090	+	0.482148i	$0.160143\pi$
$174$	−16.3039			−1.23600
$175$	−12.7528	+	3.51653i	−0.964021	+	0.265825i
$176$	−1.04034			−0.0784187
$177$	23.7337	−	36.5467i	1.78394	−	2.74702i
$178$	−4.17849	+	10.8853i	−0.313191	+	0.815891i
$179$	−4.56303	−	10.2487i	−0.341057	−	0.766026i	−0.999905	−	0.0137506i	$-0.995623\pi$
$179$	−4.56303	−	10.2487i	−0.341057	−	0.766026i	0.658849	−	0.752276i	$-0.271044\pi$
$180$	13.6247	−	9.44750i	1.01553	−	0.704175i
$181$	1.45274	+	1.99952i	0.107981	+	0.148623i	0.859587	−	0.510989i	$-0.170721\pi$
$181$	1.45274	+	1.99952i	0.107981	+	0.148623i	−0.751606	+	0.659612i	$0.770721\pi$
$182$	5.89094	+	10.2280i	0.436665	+	0.758147i
$183$	8.87040	+	1.40493i	0.655719	+	0.103856i
$184$	3.55123	+	3.19754i	0.261800	+	0.235726i
$185$	3.20152	−	4.69991i	0.235381	−	0.345544i
$186$	11.3589	+	12.6154i	0.832877	+	0.925003i
$187$	2.81674	−	0.147619i	0.205980	−	0.0107950i
$188$	10.4800	+	5.33981i	0.764331	+	0.389446i
$189$	17.0778	+	33.6034i	1.24223	+	2.44429i
$190$	−7.24974	−	0.540303i	−0.525951	−	0.0391977i
$191$	−6.26834	+	6.96170i	−0.453561	+	0.503731i	−0.925943	−	0.377663i	$-0.876728\pi$
$191$	−6.26834	+	6.96170i	−0.453561	+	0.503731i	0.472382	+	0.881394i	$0.343394\pi$
$192$	−2.03093	+	2.50799i	−0.146570	+	0.180999i
$193$	11.8247	−	3.16842i	0.851160	−	0.228068i	0.193237	−	0.981152i	$-0.438102\pi$
$193$	11.8247	−	3.16842i	0.851160	−	0.228068i	0.657924	+	0.753084i	$0.271435\pi$
$194$	−5.13006	−	2.28405i	−0.368317	−	0.163985i
$195$	−32.0827	+	2.65898i	−2.29749	+	0.190413i
$196$	2.83385	+	6.40073i	0.202418	+	0.457195i
$197$	1.78531	−	0.282765i	0.127198	−	0.0201462i	−0.0925109	−	0.995712i	$-0.529489\pi$
$197$	1.78531	−	0.282765i	0.127198	−	0.0201462i	0.219709	+	0.975566i	$0.429489\pi$
$198$	6.46935	+	4.20124i	0.459757	+	0.298569i
$199$	4.05105	−	7.01663i	0.287171	−	0.497395i	−0.685962	−	0.727637i	$-0.740618\pi$
$199$	4.05105	−	7.01663i	0.287171	−	0.497395i	0.973133	+	0.230242i	$0.0739517\pi$
$200$	0.563897	+	4.96810i	0.0398735	+	0.351298i
$201$	14.9252	−	8.61709i	1.05275	−	0.607803i
$202$	−16.6786	+	8.49818i	−1.17350	+	0.597930i
$203$	10.8056	+	7.86789i	0.758402	+	0.552218i
$204$	5.14290	−	7.07859i	0.360075	−	0.495600i
$205$	−3.81132	−	1.33188i	−0.266194	−	0.0930228i
$206$	−16.1669	+	1.69921i	−1.12640	+	0.118389i
$207$	−9.17053	−	34.2249i	−0.637396	−	2.37879i
$208$	4.16486	−	1.59874i	0.288781	−	0.110853i
$209$	−1.04520	−	3.21679i	−0.0722978	−	0.222510i
$210$	−19.0872	−	0.440423i	−1.31714	−	0.0303921i
$211$	−1.31322	+	4.04166i	−0.0904055	+	0.278239i	−0.986029	−	0.166573i	$-0.946730\pi$
$211$	−1.31322	+	4.04166i	−0.0904055	+	0.278239i	0.895624	+	0.444813i	$0.146730\pi$
$212$	0.350824	+	6.69411i	0.0240947	+	0.459753i
$213$	−21.4009	+	13.8979i	−1.46636	+	0.952268i
$214$	−2.70332	+	2.43408i	−0.184795	+	0.166390i
$215$	2.09778	+	15.4388i	0.143067	+	1.05292i
$216$	13.5497	−	4.40257i	0.921941	−	0.299557i
$217$	−1.44034	−	13.8425i	−0.0977770	−	0.939688i
$218$	−2.82455	−	2.82455i	−0.191303	−	0.191303i
$219$	22.0699	−	49.5697i	1.49134	−	3.34961i
$220$	−2.03975	+	1.11848i	−0.137520	+	0.0754077i
$221$	−11.0496	+	4.91958i	−0.743274	+	0.330927i
$222$	6.37828	−	5.16503i	0.428082	−	0.346654i
$223$	9.82033	+	19.2735i	0.657618	+	1.29065i	0.943178	+	0.332287i	$0.107820\pi$
$223$	9.82033	+	19.2735i	0.657618	+	1.29065i	−0.285560	+	0.958361i	$0.592180\pi$
$224$	2.55631	−	0.682112i	0.170801	−	0.0455755i
$225$	16.5563	−	33.1713i	1.10375	−	2.21142i
$226$	−2.77553	−	4.80736i	−0.184626	−	0.319781i
$227$	0.111545	−	2.12840i	0.00740348	−	0.141267i	−0.992427	−	0.122838i	$-0.960800\pi$
$227$	0.111545	−	2.12840i	0.00740348	−	0.141267i	0.999830	−	0.0184285i	$-0.00586631\pi$
$228$	−9.79524	−	3.76004i	−0.648706	−	0.249015i
$229$	−3.13883	+	29.8640i	−0.207420	+	1.97347i	0.0205170	+	0.999790i	$0.493469\pi$
$229$	−3.13883	+	29.8640i	−0.207420	+	1.97347i	−0.227937	+	0.973676i	$0.573198\pi$
$230$	10.4004	+	2.45131i	0.685782	+	0.161635i
$231$	−3.17467	−	8.29608i	−0.208878	−	0.545842i
$232$	3.57235	−	3.57235i	0.234536	−	0.234536i
$233$	−1.04027	−	2.70999i	−0.0681502	−	0.177537i	0.895276	−	0.445513i	$-0.146979\pi$
$233$	−1.04027	−	2.70999i	−0.0681502	−	0.177537i	−0.963426	+	0.267976i	$0.913645\pi$
$234$	−32.3554	−	6.87735i	−2.11514	−	0.449586i
$235$	26.2884	−	0.797572i	1.71487	−	0.0520278i
$236$	2.80746	+	13.2080i	0.182750	+	0.859770i
$237$	17.4444	−	34.2366i	1.13314	−	2.22391i
$238$	−6.82445	+	2.20955i	−0.442363	+	0.143224i
$239$	−5.42407	−	1.76239i	−0.350854	−	0.113999i	0.128288	−	0.991737i	$-0.459052\pi$
$239$	−5.42407	−	1.76239i	−0.350854	−	0.113999i	−0.479142	+	0.877738i	$0.659052\pi$
$240$	−1.28559	+	7.10076i	−0.0829845	+	0.458352i
$241$	1.73737	−	8.17367i	0.111914	−	0.526512i	−0.886099	−	0.463496i	$-0.846595\pi$
$241$	1.73737	−	8.17367i	0.111914	−	0.526512i	0.998013	−	0.0630161i	$-0.0200719\pi$
$242$	7.70749	+	6.24140i	0.495456	+	0.401213i
$243$	−32.6981	−	8.76143i	−2.09758	−	0.562046i
$244$	−2.25143	+	1.63576i	−0.144133	+	0.104719i
$245$	12.4376	+	9.50290i	0.794611	+	0.607118i
$246$	−4.71401	−	3.42493i	−0.300554	−	0.218365i
$247$	9.12769	+	11.2718i	0.580781	+	0.717205i
$248$	−5.25300	−	0.275298i	−0.333566	−	0.0174814i
$249$	9.78359	+	5.64856i	0.620010	+	0.357963i
$250$	6.44684	+	9.13446i	0.407734	+	0.577714i
$251$		−	22.1994i		−	1.40121i	−0.713549	−	0.700606i	$-0.752913\pi$
$251$		−	22.1994i		−	1.40121i	0.713549	−	0.700606i	$-0.247087\pi$
$252$	−18.6510	−	6.08153i	−1.17490	−	0.383100i
$253$	0.777702	+	4.91022i	0.0488937	+	0.308703i
$254$	−8.76557	−	0.921299i	−0.550001	−	0.0578074i
$255$	2.47319	−	19.4078i	0.154877	−	1.21536i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	1.61424	−	6.02444i	0.100694	−	0.375794i	−0.897127	−	0.441772i	$-0.854350\pi$
$257$	1.61424	−	6.02444i	0.100694	−	0.375794i	0.997821	+	0.0659778i	$0.0210166\pi$
$258$	−3.51768	+	22.2098i	−0.219001	+	1.38272i
$259$	−6.71977	+	0.345159i	−0.417546	+	0.0214471i
$260$	6.44702	−	7.61224i	0.399827	−	0.472091i
$261$	−36.6410	+	7.78828i	−2.26802	+	0.482082i
$262$	2.97647	+	4.58337i	0.183887	+	0.283161i
$263$	−5.11425	−	7.87525i	−0.315358	−	0.485609i	0.645075	−	0.764119i	$-0.276826\pi$
$263$	−5.11425	−	7.87525i	−0.315358	−	0.485609i	−0.960433	+	0.278510i	$0.910159\pi$
$264$	−3.28400	+	0.698037i	−0.202116	+	0.0429612i
$265$	7.88472	+	12.7476i	0.484354	+	0.783081i
$266$	4.67737	+	7.21894i	0.286788	+	0.442622i
$267$	−5.88635	+	37.1649i	−0.360239	+	2.27446i
$268$	−1.38218	+	5.15835i	−0.0844299	+	0.315097i
$269$	0.143900	+	1.36912i	0.00877375	+	0.0834767i	0.998033	−	0.0626980i	$-0.0199705\pi$
$269$	0.143900	+	1.36912i	0.00877375	+	0.0834767i	−0.989259	+	0.146175i	$0.953304\pi$
$270$	21.8330	−	23.1993i	1.32872	−	1.41186i
$271$	9.07659	+	0.953988i	0.551363	+	0.0579506i	0.376114	−	0.926573i	$-0.377260\pi$
$271$	9.07659	+	0.953988i	0.551363	+	0.0579506i	0.175249	+	0.984524i	$0.443927\pi$
$272$	0.424129	+	2.67785i	0.0257166	+	0.162368i
$273$	25.4583	+	28.3336i	1.54081	+	1.71482i
$274$		−	14.6551i		−	0.885345i
$275$	−2.79675	+	4.38588i	−0.168650	+	0.264479i
$276$	13.3555	+	7.71078i	0.803904	+	0.464134i
$277$	−11.3836	−	0.596589i	−0.683974	−	0.0358456i	−0.292816	−	0.956169i	$-0.594592\pi$
$277$	−11.3836	−	0.596589i	−0.683974	−	0.0358456i	−0.391158	+	0.920323i	$0.627926\pi$
$278$	−7.20956	−	8.90307i	−0.432401	−	0.533971i
$279$	31.5540	+	22.9253i	1.88909	+	1.37250i
$280$	4.27869	−	4.08569i	0.255701	−	0.244166i
$281$	20.4483	−	14.8566i	1.21984	−	0.886268i	0.223756	−	0.974645i	$-0.428168\pi$
$281$	20.4483	−	14.8566i	1.21984	−	0.886268i	0.996087	+	0.0883775i	$0.0281682\pi$
$282$	36.6646	+	9.82424i	2.18334	+	0.585025i
$283$	−2.81387	−	2.27863i	−0.167267	−	0.135450i	0.542032	−	0.840358i	$-0.317655\pi$
$283$	−2.81387	−	2.27863i	−0.167267	−	0.135450i	−0.709299	+	0.704908i	$0.750988\pi$
$284$	1.64398	−	7.73430i	0.0975521	−	0.458946i
$285$	−23.2475	+	3.15879i	−1.37706	+	0.187111i
$286$	4.41399	+	1.43419i	0.261005	+	0.0848055i
$287$	1.47146	+	4.54476i	0.0868574	+	0.268269i
$288$	−3.36620	+	6.60654i	−0.198355	+	0.389294i
$289$	2.00619	+	9.43839i	0.118011	+	0.555199i
$290$	3.16348	−	10.8448i	0.185766	−	0.636828i
$291$	−17.7264	−	3.76786i	−1.03914	−	0.220876i
$292$	6.02549	+	15.6969i	0.352615	+	0.918594i
$293$	−14.9340	+	14.9340i	−0.872453	+	0.872453i	−0.992739	−	0.120286i	$-0.961619\pi$
$293$	−14.9340	+	14.9340i	−0.872453	+	0.872453i	0.120286	+	0.992739i	$0.461619\pi$
$294$	13.2402	+	18.3035i	0.772182	+	1.06748i
$295$	19.7045	+	22.8780i	1.14724	+	1.33201i
$296$	−0.265835	+	2.52925i	−0.0154513	+	0.147010i
$297$	13.8373	+	5.31164i	0.802922	+	0.308213i
$298$	0.376845	−	7.19063i	0.0218300	−	0.416542i
$299$	−10.6592	−	18.4622i	−0.616436	−	1.06770i
$300$	5.11347	+	15.3042i	0.295226	+	0.883591i
$301$	13.0493	−	13.0222i	0.752148	−	0.750585i
$302$	−2.46953	−	4.84672i	−0.142105	−	0.278898i
$303$	−46.9467	+	38.0167i	−2.69702	+	2.18400i
$304$	2.97009	−	1.32237i	0.170347	−	0.0758432i
$305$	−2.65565	+	5.62767i	−0.152062	+	0.322239i
$306$	8.17659	−	18.3649i	0.467425	−	1.04985i
$307$	−8.22791	−	8.22791i	−0.469591	−	0.469591i	0.432191	−	0.901782i	$-0.357741\pi$
$307$	−8.22791	−	8.22791i	−0.469591	−	0.469591i	−0.901782	+	0.432191i	$0.857741\pi$
$308$	2.51335	+	1.12215i	0.143212	+	0.0639405i
$309$	−49.8932	+	16.2113i	−2.83832	+	0.922227i
$310$	−10.5953	+	5.10777i	−0.601771	+	0.290102i
$311$	−1.80050	+	1.62118i	−0.102097	+	0.0919287i	−0.718599	−	0.695425i	$-0.755216\pi$
$311$	−1.80050	+	1.62118i	−0.102097	+	0.0919287i	0.616501	+	0.787354i	$0.288549\pi$
$312$	12.0743	−	7.84117i	0.683575	−	0.443919i
$313$	1.23521	+	23.5693i	0.0698184	+	1.33221i	0.778927	+	0.627115i	$0.215764\pi$
$313$	1.23521	+	23.5693i	0.0698184	+	1.33221i	−0.709108	+	0.705100i	$0.750902\pi$
$314$	4.19758	−	12.9188i	0.236883	−	0.729051i
$315$	−43.1063	+	8.12802i	−2.42877	+	0.457962i
$316$	3.67933	+	11.3238i	0.206979	+	0.637015i
$317$	19.7403	−	7.57758i	1.10872	−	0.425599i	0.266015	−	0.963969i	$-0.414293\pi$
$317$	19.7403	−	7.57758i	1.10872	−	0.425599i	0.842709	+	0.538370i	$0.180960\pi$
$318$	5.59897	+	20.8956i	0.313975	+	1.17177i
$319$	5.22709	−	0.549389i	0.292661	−	0.0307599i
$320$	−1.27416	−	1.83753i	−0.0712277	−	0.102721i
$321$	−6.90027	+	9.49740i	−0.385135	+	0.530093i
$322$	−5.13040	−	11.5554i	−0.285906	−	0.643957i
$323$	−7.85393	+	4.00178i	−0.437004	+	0.222665i
$324$	20.5539	−	11.8668i	1.14188	−	0.659267i
$325$	4.45640	−	21.8562i	0.247196	−	1.21236i
$326$	−5.09283	+	8.82103i	−0.282066	+	0.488552i
$327$	−10.8113	−	7.02095i	−0.597867	−	0.388259i
$328$	1.78332	−	0.282450i	0.0984674	−	0.0155957i
$329$	−19.5588	−	24.2045i	−1.07831	−	1.33444i
$330$	−5.68832	+	4.89926i	−0.313132	+	0.269695i
$331$	−8.58655	−	3.82298i	−0.471959	−	0.210130i	0.156953	−	0.987606i	$-0.449833\pi$
$331$	−8.58655	−	3.82298i	−0.471959	−	0.210130i	−0.628912	+	0.777476i	$0.716500\pi$
$332$	−3.38133	+	0.906026i	−0.185575	+	0.0497246i
$333$	11.8670	−	14.6546i	0.650310	−	0.803066i
$334$	4.88533	−	5.42571i	0.267313	−	0.296881i
$335$	2.83581	+	11.5997i	0.154937	+	0.633760i
$336$	7.61172	−	3.86840i	0.415254	−	0.211038i
$337$	−3.63579	−	1.85253i	−0.198054	−	0.100914i	0.352151	−	0.935943i	$-0.385450\pi$
$337$	−3.63579	−	1.85253i	−0.198054	−	0.100914i	−0.550205	+	0.835030i	$0.685450\pi$
$338$	−6.89259	+	0.361226i	−0.374908	+	0.0196481i
$339$	−11.9870	−	13.3129i	−0.651044	−	0.723058i
$340$	3.71054	+	4.79434i	0.201232	+	0.260009i
$341$	−4.06680	−	3.66176i	−0.220229	−	0.198295i
$342$	−23.8097	−	3.77108i	−1.28748	−	0.203917i
$343$	0.0577992	−	18.5202i	0.00312086	−	0.999995i
$344$	−4.09562	−	5.63714i	−0.220821	−	0.303934i
$345$	34.4753	+	0.759610i	1.85609	+	0.0408960i
$346$	0.778817	+	1.74925i	0.0418695	+	0.0940404i
$347$	−8.23834	+	21.4616i	−0.442257	+	1.15212i	0.513533	+	0.858070i	$0.328336\pi$
$347$	−8.23834	+	21.4616i	−0.442257	+	1.15212i	−0.955790	+	0.294050i	$0.904997\pi$
$348$	8.87976	−	13.6736i	0.476005	−	0.732984i
$349$	−24.4907			−1.31096			−0.655479	−	0.755213i	$-0.727533\pi$
$349$	−24.4907			−1.31096			−0.655479	+	0.755213i	$0.727533\pi$
$350$	3.99647	−	12.6106i	0.213620	−	0.674067i
$351$	−63.5584			−3.39249
$352$	0.566611	−	0.872504i	0.0302004	−	0.0465046i
$353$	6.40509	−	16.6858i	0.340908	−	0.888097i	−0.650760	−	0.759283i	$-0.725550\pi$
$353$	6.40509	−	16.6858i	0.340908	−	0.888097i	0.991669	−	0.128814i	$-0.0411169\pi$
$354$	17.7244	+	39.8096i	0.942039	+	2.11585i
$355$	−5.09193	−	16.9317i	−0.270251	−	0.898642i
$356$	−6.85344	−	9.43296i	−0.363232	−	0.499946i
$357$	−20.0599	+	11.5538i	−1.06168	+	0.611492i
$358$	11.0805	+	1.75498i	0.585623	+	0.0927536i
$359$	19.8952	+	17.9138i	1.05003	+	0.945452i	0.998583	−	0.0532234i	$-0.0169496\pi$
$359$	19.8952	+	17.9138i	1.05003	+	0.945452i	0.0514484	+	0.998676i	$0.483616\pi$
$360$	0.502787	+	16.5721i	0.0264992	+	0.873428i
$361$	−5.64069	−	6.26462i	−0.296878	−	0.329717i
$362$	−2.46816	+	0.129351i	−0.129724	+	0.00679853i
$363$	28.5177	+	14.5305i	1.49679	+	0.762653i
$364$	−11.7863	−	0.629991i	−0.617771	−	0.0330205i
$365$	28.6897	+	24.2982i	1.50169	+	1.27182i
$366$	−6.00944	+	6.67416i	−0.314119	+	0.348864i
$367$	22.3963	−	27.6571i	1.16908	−	1.44369i	0.296624	−	0.954994i	$-0.404139\pi$
$367$	22.3963	−	27.6571i	1.16908	−	1.44369i	0.872454	−	0.488697i	$-0.162527\pi$
$368$	−4.61582	+	1.23680i	−0.240616	+	0.0644729i
$369$	−12.2302	−	5.44523i	−0.636678	−	0.283467i
$370$	2.19800	+	5.24478i	0.114269	+	0.272663i
$371$	6.37297	−	16.5507i	0.330868	−	0.859268i
$372$	−16.7666	+	2.65558i	−0.869310	+	0.137685i
$373$	−0.995664	−	0.646592i	−0.0515535	−	0.0334793i	0.518605	−	0.855014i	$-0.326452\pi$
$373$	−0.995664	−	0.646592i	−0.0515535	−	0.0334793i	−0.570158	+	0.821535i	$0.693118\pi$
$374$	−1.41030	+	2.44271i	−0.0729249	+	0.126310i
$375$	26.4794	+	24.5087i	1.36739	+	1.26563i
$376$	−10.1861	+	5.88098i	−0.525310	+	0.303288i
$377$	−20.0816	+	10.2321i	−1.03426	+	0.526980i
$378$	−37.4834	−	3.97910i	−1.92794	−	0.204663i
$379$	−5.86674	+	8.07487i	−0.301354	+	0.414778i	−0.932661	−	0.360755i	$-0.882519\pi$
$379$	−5.86674	+	8.07487i	−0.301354	+	0.414778i	0.631306	+	0.775533i	$0.282519\pi$
$380$	4.40163	−	5.78587i	0.225799	−	0.296809i
$381$	−28.2881	+	2.97320i	−1.44924	+	0.152322i
$382$	−2.42459	−	9.04869i	−0.124053	−	0.462971i
$383$	−14.3451	+	5.50659i	−0.733003	+	0.281373i	−0.696099	−	0.717945i	$-0.745083\pi$
$383$	−14.3451	+	5.50659i	−0.733003	+	0.281373i	−0.0369033	+	0.999319i	$0.511749\pi$
$384$	−0.997254	−	3.06923i	−0.0508909	−	0.156626i
$385$	6.13424	−	0.501974i	0.312630	−	0.0255830i
$386$	−3.78293	+	11.6427i	−0.192546	+	0.592596i
$387$	2.70392	+	51.5939i	0.137448	+	2.62267i
$388$	4.70959	−	3.05845i	0.239093	−	0.155269i
$389$	−7.04198	+	6.34063i	−0.357043	+	0.321483i	−0.828058	−	0.560642i	$-0.810554\pi$
$389$	−7.04198	+	6.34063i	−0.357043	+	0.321483i	0.471015	+	0.882125i	$0.343888\pi$
$390$	15.2435	−	28.3550i	0.771884	−	1.43581i
$391$	12.3219	−	4.00362i	0.623144	−	0.202472i
$392$	−6.91153	−	1.10942i	−0.349085	−	0.0560344i
$393$	12.4710	+	12.4710i	0.629079	+	0.629079i
$394$	−0.735202	+	1.65129i	−0.0370389	+	0.0831908i
$395$	19.3882	+	18.2464i	0.975525	+	0.918075i
$396$	−7.04692	+	3.13749i	−0.354121	+	0.157665i
$397$	−21.0260	+	17.0265i	−1.05526	+	0.854535i	−0.989678	−	0.143312i	$-0.954225\pi$
$397$	−21.0260	+	17.0265i	−1.05526	+	0.854535i	−0.0655855	+	0.997847i	$0.520891\pi$
$398$	3.67828	+	7.21903i	0.184375	+	0.361857i
$399$	19.6085	+	19.6494i	0.981654	+	0.983699i
$400$	−4.47372	−	2.23290i	−0.223686	−	0.111645i
$401$	−10.0459	−	17.4001i	−0.501670	−	0.868917i	−0.999998	−	0.00192913i	$-0.999386\pi$
$401$	−10.0459	−	17.4001i	−0.501670	−	0.868917i	0.498328	−	0.866988i	$-0.333947\pi$
$402$	−0.901967	+	17.2106i	−0.0449860	+	0.858385i
$403$	21.9080	+	8.40971i	1.09132	+	0.418918i
$404$	1.95665	−	18.6163i	0.0973471	−	0.926196i
$405$	27.5409	−	45.3643i	1.36852	−	2.25417i
$406$	−12.4837	+	4.77715i	−0.619556	+	0.237086i
$407$	−1.87085	+	1.87085i	−0.0927345	+	0.0927345i
$408$	3.13558	+	8.16847i	0.155234	+	0.404400i
$409$	28.7313	+	6.10703i	1.42067	+	0.301973i	0.853271	−	0.521468i	$-0.174616\pi$
$409$	28.7313	+	6.10703i	1.42067	+	0.301973i	0.567401	+	0.823441i	$0.307949\pi$
$410$	3.19280	−	2.47104i	0.157681	−	0.122036i
$411$	−9.83309	−	46.2611i	−0.485031	−	2.28189i
$412$	7.38003	−	14.4841i	0.363588	−	0.713582i
$413$	7.46418	−	34.9374i	0.367288	−	1.71916i
$414$	33.6980	+	10.9491i	1.65617	+	0.538121i
$415$	−5.65554	+	5.41169i	−0.277620	+	0.265649i
$416$	−0.927530	+	4.36368i	−0.0454759	+	0.213947i
$417$	−28.7318	−	23.2666i	−1.40700	−	1.13937i
$418$	3.26708	+	0.875412i	0.159798	+	0.0428178i
$419$	9.67541	−	7.02959i	0.472675	−	0.343418i	−0.325808	−	0.945436i	$-0.605636\pi$
$419$	9.67541	−	7.02959i	0.472675	−	0.343418i	0.798483	+	0.602018i	$0.205636\pi$
$420$	10.7650	−	15.7680i	0.525278	−	0.769399i
$421$	−9.85571	−	7.16059i	−0.480338	−	0.348986i	0.321119	−	0.947039i	$-0.395941\pi$
$421$	−9.85571	−	7.16059i	−0.480338	−	0.348986i	−0.801456	+	0.598053i	$0.795941\pi$
$422$	−2.67439	−	3.30260i	−0.130187	−	0.160768i
$423$	87.0917	+	4.56428i	4.23455	+	0.221923i
$424$	−5.80523	−	3.35165i	−0.281927	−	0.162770i
$425$	12.4295	+	5.41080i	0.602918	+	0.262462i
$426$		−	25.5176i		−	1.23633i
$427$	7.20360	−	1.52334i	0.348606	−	0.0737196i
$428$	−0.569058	−	3.59289i	−0.0275064	−	0.173669i
$429$	14.8958	+	1.56561i	0.719174	+	0.0755882i
$430$	−14.0906	−	6.64923i	−0.679509	−	0.320654i
$431$	3.33340	+	31.7152i	0.160564	+	1.52767i	0.717175	+	0.696893i	$0.245435\pi$
$431$	3.33340	+	31.7152i	0.160564	+	1.52767i	−0.556611	+	0.830774i	$0.687898\pi$
$432$	−3.68740	+	13.7616i	−0.177410	+	0.662103i
$433$	1.05494	−	6.66060i	0.0506970	−	0.320088i	−0.949287	−	0.314411i	$-0.898193\pi$
$433$	1.05494	−	6.66060i	0.0506970	−	0.320088i	0.999984	−	0.00567699i	$-0.00180705\pi$
$434$	12.3937	+	6.33118i	0.594919	+	0.303906i
$435$	2.70951	−	36.3559i	0.129911	−	1.74313i
$436$	3.90722	−	0.830506i	0.187122	−	0.0397740i
$437$	−8.46162	−	13.0298i	−0.404774	−	0.623298i
$438$	29.5526	+	45.5070i	1.41208	+	2.17441i
$439$	9.67498	−	2.05648i	0.461762	−	0.0981505i	0.0288440	−	0.999584i	$-0.490817\pi$
$439$	9.67498	−	2.05648i	0.461762	−	0.0981505i	0.432918	+	0.901433i	$0.357484\pi$
$440$	0.172892	−	2.31984i	0.00824228	−	0.110594i
$441$	38.4990	+	34.8100i	1.83329	+	1.65762i
$442$	1.89211	−	11.9463i	0.0899987	−	0.568229i
$443$	−4.98100	+	18.5893i	−0.236654	+	0.883206i	0.740742	+	0.671790i	$0.234474\pi$
$443$	−4.98100	+	18.5893i	−0.236654	+	0.883206i	−0.977396	+	0.211416i	$0.932193\pi$
$444$	0.857898	+	8.16235i	0.0407140	+	0.387368i
$445$	−23.5786	−	11.1266i	−1.11773	−	0.527449i
$446$	−21.5126	−	2.26107i	−1.01865	−	0.107065i
$447$	−3.63512	−	22.9512i	−0.171935	−	1.08556i
$448$	−0.820199	+	2.51541i	−0.0387508	+	0.118842i
$449$			12.0364i			0.568035i	0.958819	+	0.284017i	$0.0916673\pi$
$449$			12.0364i			0.568035i	−0.958819	+	0.284017i	$0.908333\pi$
$450$	18.8026	+	31.9516i	0.886362	+	1.50621i
$451$	1.62673	+	0.939194i	0.0765998	+	0.0442249i
$452$	5.54346	+	0.290520i	0.260742	+	0.0136649i
$453$	−11.0475	−	13.6425i	−0.519055	−	0.640979i
$454$	1.72427	+	1.25276i	0.0809242	+	0.0587948i
$455$	−23.7862	+	11.4364i	−1.11511	+	0.536144i
$456$	8.48830	−	6.16711i	0.397501	−	0.288802i
$457$	−28.7939	−	7.71530i	−1.34692	−	0.360907i	−0.487924	−	0.872886i	$-0.662246\pi$
$457$	−28.7939	−	7.71530i	−1.34692	−	0.360907i	−0.858998	+	0.511979i	$0.828912\pi$
$458$	−23.3365	−	18.8975i	−1.09044	−	0.883023i
$459$	8.03098	−	37.7828i	0.374854	−	1.76355i
$460$	−7.72031	+	7.38743i	−0.359961	+	0.344441i
$461$	−1.49312	−	0.485145i	−0.0695416	−	0.0225954i	0.274040	−	0.961718i	$-0.411640\pi$
$461$	−1.49312	−	0.485145i	−0.0695416	−	0.0225954i	−0.343581	+	0.939123i	$0.611640\pi$
$462$	8.68673	+	1.85587i	0.404143	+	0.0863428i
$463$	8.32467	−	16.3381i	0.386880	−	0.759295i	−0.612637	−	0.790364i	$-0.709891\pi$
$463$	8.32467	−	16.3381i	0.386880	−	0.759295i	0.999517	+	0.0310691i	$0.00989120\pi$
$464$	1.05038	+	4.94167i	0.0487629	+	0.229411i
$465$	−30.0185	+	23.2326i	−1.39207	+	1.07738i
$466$	2.83936	+	0.603524i	0.131531	+	0.0279577i
$467$	−3.22485	−	8.40101i	−0.149228	−	0.388752i	0.838507	−	0.544891i	$-0.183429\pi$
$467$	−3.22485	−	8.40101i	−0.149228	−	0.388752i	−0.987735	+	0.156138i	$0.950095\pi$
$468$	23.3898	−	23.3898i	1.08120	−	1.08120i
$469$	8.90319	−	10.9712i	0.411111	−	0.506601i
$470$	−13.6488	+	22.4817i	−0.629572	+	1.03700i
$471$	4.58220	−	43.5968i	0.211137	−	2.00883i
$472$	−12.6062	−	4.83908i	−0.580249	−	0.222737i
$473$	0.379383	−	7.23905i	0.0174440	−	0.332852i
$474$	19.2123	+	33.2767i	0.882451	+	1.52845i
$475$	2.40963	−	16.0763i	0.110561	−	0.737630i
$476$	1.86378	−	6.92688i	0.0854260	−	0.317493i
$477$	22.5646	+	44.2856i	1.03316	+	2.02770i
$478$	4.43222	−	3.58914i	0.202725	−	0.164164i
$479$	14.3175	−	6.37458i	0.654185	−	0.291262i	−0.0526787	−	0.998612i	$-0.516776\pi$
$479$	14.3175	−	6.37458i	0.654185	−	0.291262i	0.706864	+	0.707349i	$0.250109\pi$
$480$	−5.25501	−	4.94553i	−0.239857	−	0.225732i
$481$	4.61466	−	10.3647i	0.210410	−	0.472590i
$482$	5.90878	+	5.90878i	0.269137	+	0.269137i
$483$	−23.9482	−	33.0341i	−1.08968	−	1.50310i
$484$	−9.43228	+	3.06473i	−0.428740	+	0.139306i
$485$	5.94571	−	11.0599i	0.269981	−	0.502202i
$486$	25.1566	−	22.6511i	1.14113	−	1.02748i
$487$	−9.38524	+	6.09485i	−0.425286	+	0.276184i	−0.739485	−	0.673173i	$-0.764931\pi$
$487$	−9.38524	+	6.09485i	−0.425286	+	0.276184i	0.314199	+	0.949357i	$0.398264\pi$
$488$	−0.145647	−	2.77910i	−0.00659311	−	0.125804i
$489$	−10.1577	+	31.2621i	−0.459346	+	1.41372i
$490$	−14.7438	+	5.25543i	−0.666058	+	0.237416i
$491$	12.6815	+	39.0297i	0.572309	+	1.76139i	0.645165	+	0.764044i	$0.276789\pi$
$491$	12.6815	+	39.0297i	0.572309	+	1.76139i	−0.0728557	+	0.997342i	$0.523211\pi$
$492$	5.43982	−	2.08815i	0.245246	−	0.0941411i
$493$	−3.54512	−	13.2306i	−0.159664	−	0.595876i
$494$	−14.4246	+	1.51609i	−0.648993	+	0.0682119i
$495$	−10.4434	+	13.7277i	−0.469396	+	0.617014i
$496$	3.09187	−	4.25560i	0.138829	−	0.191082i
$497$	−12.3142	+	16.9120i	−0.552367	+	0.758607i
$498$	−10.0658	+	5.12878i	−0.451059	+	0.229826i
$499$	−11.1280	+	6.42477i	−0.498159	+	0.287612i	−0.727953	−	0.685627i	$-0.759528\pi$
$499$	−11.1280	+	6.42477i	−0.498159	+	0.287612i	0.229794	+	0.973239i	$0.426195\pi$
$500$	−11.1720	+	0.431790i	−0.499627	+	0.0193102i
$501$	11.7808	−	20.4050i	0.526329	−	0.911628i
$502$	18.6180	+	12.0906i	0.830960	+	0.539632i
$503$	−15.9444	+	2.52535i	−0.710927	+	0.112600i	−0.501416	−	0.865206i	$-0.667187\pi$
$503$	−15.9444	+	2.52535i	−0.710927	+	0.112600i	−0.209511	+	0.977806i	$0.567187\pi$
$504$	15.2584	−	12.3298i	0.679665	−	0.549212i
$505$	−16.1782	−	38.6037i	−0.719920	−	1.71784i
$506$	−4.54162	−	2.02206i	−0.201900	−	0.0898915i
$507$	−21.5152	+	5.76498i	−0.955523	+	0.256032i
$508$	5.54674	−	6.84965i	0.246097	−	0.303904i
$509$	15.2530	−	16.9402i	0.676077	−	0.750860i	−0.303301	−	0.952895i	$-0.598089\pi$
$509$	15.2530	−	16.9402i	0.676077	−	0.750860i	0.979378	+	0.202035i	$0.0647555\pi$
$510$	14.9297	+	12.6444i	0.661100	+	0.559905i
$511$	2.37437	−	44.4215i	0.105036	−	1.96509i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−46.2560	+	2.42418i	−2.04225	+	0.107030i
$514$	4.17334	+	4.63497i	0.184078	+	0.204440i
$515$	−1.10231	−	36.3326i	−0.0485734	−	1.60101i
$516$	−16.7108	−	15.0465i	−0.735653	−	0.662385i
$517$	−12.0858	−	1.91420i	−0.531533	−	0.0841865i
$518$	3.37037	−	5.82366i	0.148086	−	0.255877i
$519$	3.63215	+	4.99923i	0.159434	+	0.219442i
$520$	2.87286	+	9.55285i	0.125983	+	0.418920i
$521$	−3.52727	−	7.92238i	−0.154533	−	0.347086i	0.819644	−	0.572873i	$-0.194171\pi$
$521$	−3.52727	−	7.92238i	−0.154533	−	0.347086i	−0.974177	+	0.225787i	$0.927505\pi$
$522$	13.4243	−	34.9715i	0.587566	−	1.53066i
$523$	−0.143918	+	0.221614i	−0.00629310	+	0.00969052i	−0.841803	−	0.539785i	$-0.818506\pi$
$523$	−0.143918	+	0.221614i	−0.00629310	+	0.00969052i	0.835510	+	0.549475i	$0.185172\pi$
$524$	−5.46504			−0.238741
$525$	4.15414	−	42.4890i	0.181301	−	1.85437i
$526$	9.39016			0.409431
$527$	−7.76743	+	11.9608i	−0.338355	+	0.521021i
$528$	1.20317	−	3.13438i	0.0523614	−	0.136406i
$529$	−0.0669278	−	0.150322i	−0.00290991	−	0.00653576i
$530$	−14.9854	−	0.330180i	−0.650924	−	0.0143421i
$531$	58.8499	+	81.0000i	2.55387	+	3.51510i
$532$	−8.60179	−	0.00894836i	−0.372935	−	0.000387960i
$533$	−7.95570	−	1.26006i	−0.344600	−	0.0545792i
$534$	−27.9632	−	25.1782i	−1.21009	−	1.08957i
$535$	−4.97846	−	6.43260i	−0.215238	−	0.278106i
$536$	−3.57337	−	3.96863i	−0.154346	−	0.171419i
$537$	36.1549	−	1.89480i	1.56020	−	0.0817667i
$538$	−1.22661	−	0.624991i	−0.0528831	−	0.0269453i
$539$	−4.86160	−	5.42200i	−0.209404	−	0.233542i
$540$	7.56543	+	30.9459i	0.325564	+	1.33170i
$541$	−19.6070	+	21.7758i	−0.842972	+	0.936215i	−0.998668	−	0.0515898i	$-0.983571\pi$
$541$	−19.6070	+	21.7758i	−0.842972	+	0.936215i	0.155697	+	0.987805i	$0.450238\pi$
$542$	−5.74354	+	7.09269i	−0.246706	+	0.304657i
$543$	−7.70435	+	2.06437i	−0.330625	+	0.0885908i
$544$	−2.47683	−	1.10276i	−0.106193	−	0.0472802i
$545$	6.76782	−	5.82901i	0.289901	−	0.249687i
$546$	−37.6281	+	5.91959i	−1.61033	+	0.253335i
$547$	24.1940	−	3.83196i	1.03446	−	0.163843i	0.383962	−	0.923349i	$-0.374559\pi$
$547$	24.1940	−	3.83196i	1.03446	−	0.163843i	0.650500	+	0.759506i	$0.274559\pi$
$548$	12.2908	+	7.98172i	0.525036	+	0.340962i
$549$	−10.3172	+	17.8700i	−0.440329	+	0.762672i
$550$	−2.15509	−	4.73427i	−0.0918935	−	0.201870i
$551$	−14.2246	+	8.21258i	−0.605988	+	0.349868i
$552$	−13.7407	+	7.00124i	−0.584843	+	0.297992i
$553$	3.32543	−	31.3258i	0.141412	−	1.33211i
$554$	6.70029	−	9.22216i	0.284668	−	0.391812i
$555$	10.4574	+	15.0812i	0.443893	+	0.640160i
$556$	11.3934	−	1.19749i	0.483186	−	0.0507849i
$557$	1.91094	+	7.13172i	0.0809691	+	0.302181i	0.994520	−	0.104543i	$-0.0333379\pi$
$557$	1.91094	+	7.13172i	0.0809691	+	0.302181i	−0.913551	+	0.406724i	$0.866671\pi$
$558$	−36.4123	+	13.9774i	−1.54145	+	0.591709i
$559$	9.60578	+	29.5635i	0.406281	+	1.25040i
$560$	1.09620	+	5.81363i	0.0463231	+	0.245671i
$561$	−2.81286	+	8.65708i	−0.118759	+	0.365502i
$562$	1.32282	+	25.2408i	0.0557996	+	1.06472i
$563$	−17.9050	+	11.6276i	−0.754606	+	0.490047i	−0.863714	−	0.503983i	$-0.831867\pi$
$563$	−17.9050	+	11.6276i	−0.754606	+	0.490047i	0.109107	+	0.994030i	$0.465201\pi$
$564$	−28.2082	+	25.3988i	−1.18778	+	1.06948i
$565$	11.1811	−	5.39019i	0.470393	−	0.226767i
$566$	3.44356	−	1.11888i	0.144744	−	0.0470301i
$567$	−62.4560	+	6.49871i	−2.62291	+	0.272920i
$568$	5.59116	+	5.59116i	0.234600	+	0.234600i
$569$	16.0502	−	36.0493i	0.672858	−	1.51126i	−0.176978	−	0.984215i	$-0.556632\pi$
$569$	16.0502	−	36.0493i	0.672858	−	1.51126i	0.849835	−	0.527048i	$-0.176701\pi$
$570$	10.0123	−	21.2174i	0.419369	−	0.888698i
$571$	5.09143	−	2.26685i	0.213070	−	0.0948648i	−0.297427	−	0.954745i	$-0.596128\pi$
$571$	5.09143	−	2.26685i	0.213070	−	0.0948648i	0.510496	+	0.859880i	$0.329462\pi$
$572$	−3.60685	+	2.92077i	−0.150810	+	0.122123i
$573$	−13.7250	−	26.9368i	−0.573370	−	1.12530i
$574$	−4.61297	−	1.24119i	−0.192542	−	0.0518062i
$575$	−7.19455	+	22.7843i	−0.300034	+	0.950171i
$576$	−3.70735	−	6.42131i	−0.154473	−	0.267555i
$577$	−0.861534	+	16.4391i	−0.0358661	+	0.684367i	0.920241	+	0.391351i	$0.127992\pi$
$577$	−0.861534	+	16.4391i	−0.0358661	+	0.684367i	−0.956108	+	0.293016i	$0.905341\pi$
$578$	−9.00835	−	3.45798i	−0.374698	−	0.143833i
$579$	−4.12956	+	39.2902i	−0.171619	+	1.63284i
$580$	7.37225	+	8.55961i	0.306116	+	0.355419i
$581$	9.14622	+	1.45837i	0.379449	+	0.0605035i
$582$	12.8145	−	12.8145i	0.531176	−	0.531176i
$583$	−2.49916	−	6.51053i	−0.103505	−	0.269639i
$584$	−16.4463	−	3.49576i	−0.680552	−	0.144656i
$585$	20.7127	−	71.0058i	0.856366	−	2.93573i
$586$	−4.39107	−	20.6583i	−0.181393	−	0.853388i
$587$	2.87458	−	5.64167i	0.118646	−	0.232857i	−0.824044	−	0.566526i	$-0.808287\pi$
$587$	2.87458	−	5.64167i	0.118646	−	0.232857i	0.942690	+	0.333670i	$0.108287\pi$
$588$	−22.5617	+	1.13534i	−0.930429	+	0.0468208i
$589$	16.2648	+	5.28476i	0.670180	+	0.217755i
$590$	−29.9190	+	4.06529i	−1.23174	+	0.167365i
$591$	−1.21282	+	5.70585i	−0.0498886	+	0.234708i
$592$	−1.97642	−	1.60048i	−0.0812305	−	0.0657792i
$593$	4.42657	+	1.18609i	0.181777	+	0.0487071i	0.348559	−	0.937287i	$-0.386671\pi$
$593$	4.42657	+	1.18609i	0.181777	+	0.0487071i	−0.166782	+	0.985994i	$0.553338\pi$
$594$	−11.9911	+	8.71201i	−0.491999	+	0.357458i
$595$	−3.79291	−	15.5849i	−0.155494	−	0.638920i
$596$	5.82533	+	4.23235i	0.238615	+	0.173364i
$597$	16.4548	+	20.3200i	0.673450	+	0.831642i
$598$	21.2891	+	1.11572i	0.870578	+	0.0456250i
$599$	−27.9512	−	16.1377i	−1.14206	−	0.659367i	−0.195118	−	0.980780i	$-0.562509\pi$
$599$	−27.9512	−	16.1377i	−1.14206	−	0.659367i	−0.946939	+	0.321413i	$0.895842\pi$
$600$	−15.6202	−	4.04677i	−0.637692	−	0.165209i
$601$			9.66641i			0.394301i	0.980373	+	0.197151i	$0.0631688\pi$
$601$			9.66641i			0.394301i	−0.980373	+	0.197151i	$0.936831\pi$
$602$	3.81415	+	18.0364i	0.155453	+	0.735110i
$603$	6.19431	+	39.1093i	0.252252	+	1.59266i
$604$	5.40981	+	0.568593i	0.220122	+	0.0231357i
$605$	−15.1985	+	16.1496i	−0.617907	+	0.656573i
$606$	−6.31447	−	60.0782i	−0.256508	−	2.44051i
$607$	11.2341	−	41.9262i	0.455977	−	1.70173i	−0.229222	−	0.973374i	$-0.573618\pi$
$607$	11.2341	−	41.9262i	0.455977	−	1.70173i	0.685199	−	0.728356i	$-0.259715\pi$
$608$	−0.508595	+	3.21115i	−0.0206263	+	0.130229i
$609$	−36.2015	+	23.4560i	−1.46696	+	0.950485i
$610$	−3.27339	−	5.29226i	−0.132536	−	0.214277i
$611$	51.3254	−	10.9096i	2.07641	−	0.441354i
$612$	10.9488	+	16.8597i	0.442580	+	0.681514i
$613$	−2.22103	−	3.42008i	−0.0897064	−	0.138136i	0.790968	−	0.611857i	$-0.209577\pi$
$613$	−2.22103	−	3.42008i	−0.0897064	−	0.138136i	−0.880675	+	0.473721i	$0.842910\pi$
$614$	11.3817	−	2.41926i	0.459330	−	0.0976335i
$615$	8.42060	−	9.94251i	0.339551	−	0.400921i
$616$	−2.30999	+	1.49671i	−0.0930720	+	0.0603041i
$617$	2.47457	−	15.6238i	0.0996225	−	0.628992i	−0.886469	−	0.462788i	$-0.846849\pi$
$617$	2.47457	−	15.6238i	0.0996225	−	0.628992i	0.986091	−	0.166204i	$-0.0531509\pi$
$618$	13.5779	−	50.6732i	0.546181	−	2.03838i
$619$	2.61028	+	24.8352i	0.104916	+	0.998209i	0.912672	+	0.408692i	$0.134015\pi$
$619$	2.61028	+	24.8352i	0.104916	+	0.998209i	−0.807756	+	0.589517i	$0.799318\pi$
$620$	1.48686	−	11.6678i	0.0597139	−	0.468591i
$621$	67.7085	+	7.11645i	2.71705	+	0.285573i
$622$	−0.379012	−	2.39299i	−0.0151970	−	0.0959501i
$623$	6.38245	+	30.1814i	0.255707	+	1.20919i
$624$			14.3970i			0.576342i
$625$	−21.4402	+	12.8577i	−0.857606	+	0.514307i
$626$	−20.4396	−	11.8008i	−0.816931	−	0.471655i
$627$	10.9004	+	0.571267i	0.435321	+	0.0228142i
$628$	8.54847	+	10.5565i	0.341121	+	0.421249i
$629$	5.57829	+	4.05287i	0.222421	+	0.161598i
$630$	16.6607	−	40.5788i	0.663776	−	1.61670i
$631$	0.324924	−	0.236071i	0.0129350	−	0.00939785i	−0.581299	−	0.813690i	$-0.697455\pi$
$631$	0.324924	−	0.236071i	0.0129350	−	0.00939785i	0.594234	+	0.804292i	$0.297455\pi$
$632$	−11.5009	−	3.08165i	−0.457480	−	0.122581i
$633$	−10.6581	−	8.63075i	−0.423621	−	0.343042i
$634$	−4.39623	+	20.6826i	−0.174596	+	0.821412i
$635$	3.51112	−	19.3931i	0.139334	−	0.769592i
$636$	−20.5740	−	6.68489i	−0.815811	−	0.265073i
$637$	27.7950	+	14.2352i	1.10128	+	0.564018i
$638$	−2.38612	+	4.68302i	−0.0944674	+	0.185403i
$639$	−12.1896	−	57.3475i	−0.482213	−	2.26863i
$640$	2.23504	−	0.0678095i	0.0883477	−	0.00268041i
$641$	−18.9425	−	4.02635i	−0.748184	−	0.159031i	−0.181986	−	0.983301i	$-0.558253\pi$
$641$	−18.9425	−	4.02635i	−0.748184	−	0.159031i	−0.566197	+	0.824270i	$0.691586\pi$
$642$	−4.20704	−	10.9597i	−0.166039	−	0.432545i
$643$	4.68666	−	4.68666i	0.184824	−	0.184824i	−0.608630	−	0.793454i	$-0.708281\pi$
$643$	4.68666	−	4.68666i	0.184824	−	0.184824i	0.793454	+	0.608630i	$0.208281\pi$
$644$	12.4854	+	1.99081i	0.491993	+	0.0784488i
$645$	−48.9406	−	11.5350i	−1.92704	−	0.454191i
$646$	0.921384	−	8.76638i	0.0362514	−	0.344909i
$647$	−39.5908	−	15.1975i	−1.55647	−	0.597475i	−0.580289	−	0.814411i	$-0.697060\pi$
$647$	−39.5908	−	15.1975i	−1.55647	−	0.597475i	−0.976186	+	0.216936i	$0.930394\pi$
$648$	−1.24212	+	23.7011i	−0.0487951	+	0.931066i
$649$	−7.02393	−	12.1658i	−0.275713	−	0.477549i
$650$	15.9030	+	15.6412i	0.623767	+	0.613497i
$651$	43.3708	+	11.6695i	1.69984	+	0.457366i
$652$	−4.62419	−	9.07548i	−0.181097	−	0.355423i
$653$	7.30248	−	5.91343i	0.285768	−	0.231411i	−0.475708	−	0.879603i	$-0.657808\pi$
$653$	7.30248	−	5.91343i	0.285768	−	0.231411i	0.761476	+	0.648193i	$0.224475\pi$
$654$	11.7765	−	5.24325i	0.460499	−	0.205027i
$655$	−10.7150	+	5.87549i	−0.418671	+	0.229574i
$656$	−0.734383	+	1.64945i	−0.0286728	+	0.0644003i
$657$	88.1539	+	88.1539i	3.43921	+	3.43921i
$658$	30.9521	−	3.22064i	1.20664	−	0.125554i
$659$	13.3353	−	4.33290i	0.519469	−	0.168786i	−0.0375352	−	0.999295i	$-0.511951\pi$
$659$	13.3353	−	4.33290i	0.519469	−	0.168786i	0.557004	+	0.830510i	$0.311951\pi$
$660$	−1.01078	−	7.43895i	−0.0393446	−	0.289561i
$661$	17.4376	−	15.7009i	0.678245	−	0.610695i	−0.256275	−	0.966604i	$-0.582495\pi$
$661$	17.4376	−	15.7009i	0.678245	−	0.610695i	0.934521	+	0.355909i	$0.115829\pi$
$662$	7.88279	−	5.11914i	0.306373	−	0.198961i
$663$	−2.04286	−	38.9801i	−0.0793380	−	1.51386i
$664$	1.08175	−	3.32928i	0.0419800	−	0.129201i
$665$	−16.8747	+	9.23029i	−0.654374	+	0.357935i
$666$	5.82711	+	17.9340i	0.225796	+	0.694928i
$667$	22.5385	−	8.65174i	0.872696	−	0.334997i
$668$	1.88964	+	7.05223i	0.0731124	+	0.272859i
$669$	−69.4252	+	7.29688i	−2.68413	+	0.282114i
$670$	−11.2728	−	3.93935i	−0.435507	−	0.152190i
$671$	1.70175	−	2.34225i	0.0656952	−	0.0904217i
$672$	−0.901330	+	8.49061i	−0.0347696	+	0.327532i
$673$	−5.39918	+	2.75102i	−0.208123	+	0.106044i	−0.554945	−	0.831887i	$-0.687261\pi$
$673$	−5.39918	+	2.75102i	−0.208123	+	0.106044i	0.346822	+	0.937931i	$0.387261\pi$
$674$	3.53385	−	2.04027i	0.136119	−	0.0785883i
$675$	48.1033	+	52.5405i	1.85150	+	2.02229i
$676$	3.45103	−	5.97735i	0.132732	−	0.229898i
$677$	−28.1139	−	18.2574i	−1.08051	−	0.701689i	−0.123672	−	0.992323i	$-0.539467\pi$
$677$	−28.1139	−	18.2574i	−1.08051	−	0.701689i	−0.956834	+	0.290634i	$0.906134\pi$
$678$	17.6937	−	2.80241i	0.679523	−	0.107626i
$679$	−14.6768	+	2.30893i	−0.563245	+	0.0886087i
$680$	−6.04177	+	0.500735i	−0.231691	+	0.0192023i
$681$	6.28350	+	2.79760i	0.240784	+	0.107204i
$682$	5.28595	−	1.41637i	0.202409	−	0.0542354i
$683$	−29.9772	+	37.0187i	−1.14705	+	1.41648i	−0.253601	+	0.967309i	$0.581615\pi$
$683$	−29.9772	+	37.0187i	−1.14705	+	1.41648i	−0.893444	+	0.449174i	$0.851718\pi$
$684$	16.1304	−	17.9146i	0.616760	−	0.684981i
$685$	32.6791	+	2.43549i	1.24860	+	0.0930551i
$686$	15.5008	+	10.1353i	0.591825	+	0.386967i
$687$	−86.3450	−	43.9950i	−3.29427	−	1.67851i
$688$	6.95834	−	0.364671i	0.265284	−	0.0139030i
$689$	20.0101	+	22.2234i	0.762323	+	0.846645i
$690$	−19.4136	+	28.4997i	−0.739065	+	1.08496i
$691$	38.0763	+	34.2841i	1.44849	+	1.30423i	0.874189	+	0.485586i	$0.161394\pi$
$691$	38.0763	+	34.2841i	1.44849	+	1.30423i	0.574303	+	0.818643i	$0.305273\pi$
$692$	−1.89122	−	0.299540i	−0.0718934	−	0.0113868i
$693$	20.4088	+	0.0212311i	0.775267	+	0.000806503i
$694$	−13.5123	−	18.5981i	−0.512920	−	0.705974i
$695$	21.0509	−	14.5969i	0.798508	−	0.553692i
$696$	6.63141	+	14.8944i	0.251363	+	0.564571i
$697$	1.75430	−	4.57011i	0.0664489	−	0.173105i
$698$	13.3386	−	20.5397i	0.504874	−	0.777437i
$699$	9.36783			0.354324
$700$	8.39954	+	10.2200i	0.317473	+	0.386278i
$701$	−14.8528			−0.560982			−0.280491	−	0.959857i	$-0.590497\pi$
$701$	−14.8528			−0.560982			−0.280491	+	0.959857i	$0.590497\pi$
$702$	34.6164	−	53.3045i	1.30651	−	2.01185i
$703$	2.96310	−	7.71915i	0.111756	−	0.291133i
$704$	0.423145	+	0.950399i	0.0159479	+	0.0358195i
$705$	−28.0001	+	80.1250i	−1.05454	+	3.01768i
$706$	10.5054	+	14.4595i	0.395378	+	0.544191i
$707$	−24.8073	+	42.8645i	−0.932975	+	1.61209i
$708$	−43.0405	−	6.81694i	−1.61756	−	0.256196i
$709$	−4.68689	−	4.22009i	−0.176020	−	0.158489i	0.576412	−	0.817159i	$-0.304452\pi$
$709$	−4.68689	−	4.22009i	−0.176020	−	0.158489i	−0.752431	+	0.658671i	$0.771119\pi$
$710$	16.9734	+	4.95122i	0.637000	+	0.185816i
$711$	59.0732	+	65.6075i	2.21542	+	2.46047i
$712$	11.6438	−	0.610225i	0.436370	−	0.0228692i
$713$	−22.3969	−	11.4118i	−0.838772	−	0.427376i
$714$	1.23559	−	23.1163i	0.0462408	−	0.865106i
$715$	−3.93163	+	9.60434i	−0.147035	+	0.359182i
$716$	−7.50673	+	8.33707i	−0.280540	+	0.311571i
$717$	11.5828	−	14.3036i	0.432568	−	0.534177i
$718$	−25.8595	+	6.92903i	−0.965067	+	0.258589i
$719$	41.9668	+	18.6848i	1.56510	+	0.696827i	0.992413	−	0.122948i	$-0.0392348\pi$
$719$	41.9668	+	18.6848i	1.56510	+	0.696827i	0.572686	+	0.819775i	$0.305901\pi$
$720$	−14.1724	−	8.60416i	−0.528174	−	0.320658i
$721$	−33.4525	+	27.0317i	−1.24584	+	1.00671i
$722$	8.32609	−	1.31872i	0.309865	−	0.0490778i
$723$	22.6166	+	14.6874i	0.841120	+	0.546230i
$724$	1.23577	−	2.14042i	0.0459272	−	0.0795482i
$725$	23.6569	+	8.85645i	0.878595	+	0.328920i
$726$	−27.7182	+	16.0031i	−1.02872	+	0.593930i
$727$	−8.77521	+	4.47119i	−0.325454	+	0.165827i	−0.609082	−	0.793107i	$-0.708462\pi$
$727$	−8.77521	+	4.47119i	−0.325454	+	0.165827i	0.283628	+	0.958934i	$0.408462\pi$
$728$	6.94765	−	9.54173i	0.257497	−	0.353640i
$729$	22.3619	−	30.7785i	0.828218	−	1.13994i
$730$	−36.0037	+	10.8275i	−1.33256	+	0.400744i
$731$	−18.7880	+	1.97470i	−0.694901	+	0.0730370i
$732$	−2.32445	−	8.67495i	−0.0859140	−	0.320636i
$733$	30.2153	−	11.5986i	1.11603	−	0.428403i	0.270706	−	0.962662i	$-0.412743\pi$
$733$	30.2153	−	11.5986i	1.11603	−	0.428403i	0.845321	+	0.534260i	$0.179409\pi$
$734$	10.9973	+	33.8463i	0.405919	+	1.24929i
$735$	−43.0150	+	26.4822i	−1.58663	+	0.976812i
$736$	1.47668	−	4.54476i	0.0544312	−	0.167522i
$737$	−0.290766	−	5.54814i	−0.0107105	−	0.204369i
$738$	11.2278	−	7.29141i	0.413300	−	0.268400i
$739$	−11.8283	+	10.6502i	−0.435111	+	0.391776i	−0.857371	−	0.514699i	$-0.827904\pi$
$739$	−11.8283	+	10.6502i	−0.435111	+	0.391776i	0.422260	+	0.906475i	$0.361237\pi$
$740$	−5.59576	−	1.01311i	−0.205704	−	0.0372427i
$741$	−44.5162	+	14.4642i	−1.63535	+	0.531356i
$742$	10.4096	+	14.3590i	0.382148	+	0.527134i
$743$	2.60301	+	2.60301i	0.0954951	+	0.0954951i	0.753240	−	0.657745i	$-0.228490\pi$
$743$	2.60301	+	2.60301i	0.0954951	+	0.0954951i	−0.657745	+	0.753240i	$0.728490\pi$
$744$	6.90462	−	15.5080i	0.253136	−	0.568552i
$745$	15.9716	+	2.03531i	0.585156	+	0.0745681i
$746$	1.08455	−	0.482875i	0.0397084	−	0.0176793i
$747$	−20.1716	+	16.3346i	−0.738040	+	0.597653i
$748$	−1.28053	−	2.51317i	−0.0468207	−	0.0918908i
$749$	−2.50064	+	9.29384i	−0.0913715	+	0.339590i
$750$	−34.9765	+	8.85907i	−1.27716	+	0.323488i
$751$	−11.7104	−	20.2830i	−0.427319	−	0.740137i	0.569315	−	0.822119i	$-0.307208\pi$
$751$	−11.7104	−	20.2830i	−0.427319	−	0.740137i	−0.996634	+	0.0819819i	$0.973875\pi$
$752$	0.615573	−	11.7458i	0.0224476	−	0.428326i
$753$	66.8830	+	25.6740i	2.43735	+	0.935611i
$754$	2.35588	−	22.4147i	0.0857960	−	0.816295i
$755$	11.2180	−	4.70130i	0.408266	−	0.171098i
$756$	23.7521	−	29.2691i	0.863855	−	1.06451i
$757$	33.6393	−	33.6393i	1.22264	−	1.22264i	0.255952	−	0.966690i	$-0.417611\pi$
$757$	33.6393	−	33.6393i	1.22264	−	1.22264i	0.966690	−	0.255952i	$-0.0823888\pi$
$758$	−3.57690	−	9.31815i	−0.129919	−	0.338450i
$759$	−15.6931	−	3.33567i	−0.569623	−	0.121077i
$760$	2.45514	+	6.84273i	0.0890574	+	0.248212i
$761$	0.929961	+	4.37512i	0.0337111	+	0.158598i	0.991783	−	0.127928i	$-0.0408327\pi$
$761$	0.929961	+	4.37512i	0.0337111	+	0.158598i	−0.958072	+	0.286526i	$0.907499\pi$
$762$	12.9133	−	25.3437i	0.467798	−	0.918106i
$763$	−10.3353	−	2.20807i	−0.374161	−	0.0799373i
$764$	8.90940	+	2.89484i	0.322331	+	0.104732i
$765$	39.5928	+	21.2849i	1.43148	+	0.769556i
$766$	3.19472	−	15.0300i	0.115430	−	0.543054i
$767$	46.8151	+	37.9101i	1.69039	+	1.36885i
$768$	3.11722	+	0.835256i	0.112483	+	0.0301397i
$769$	37.7529	−	27.4291i	1.36140	−	0.989117i	0.363049	−	0.931770i	$-0.381736\pi$
$769$	37.7529	−	27.4291i	1.36140	−	0.989117i	0.998354	−	0.0573471i	$-0.0182642\pi$
$770$	−2.91996	+	5.41800i	−0.105228	+	0.195251i
$771$	16.2837	+	11.8308i	0.586444	+	0.426077i
$772$	−7.70403	−	9.51369i	−0.277274	−	0.342405i
$773$	15.7644	+	0.826175i	0.567004	+	0.0297154i	0.333685	−	0.942685i	$-0.391708\pi$
$773$	15.7644	+	0.826175i	0.567004	+	0.0297154i	0.233320	+	0.972400i	$0.425041\pi$
$774$	−44.7430	−	25.8324i	−1.60825	−	0.928526i
$775$	−9.62893	−	24.4751i	−0.345881	−	0.879170i
$776$			5.61555i			0.201586i
$777$	6.73163	−	20.6447i	0.241496	−	0.740625i
$778$	−1.48236	−	9.35925i	−0.0531452	−	0.335546i
$779$	−5.83800	−	0.613598i	−0.209168	−	0.0219844i
$780$	15.4783	+	28.2275i	0.554212	+	1.01071i
$781$	0.859859	+	8.18101i	0.0307682	+	0.292740i
$782$	−3.35326	+	12.5145i	−0.119912	+	0.447519i
$783$	11.2597	−	71.0908i	0.402388	−	2.54058i
$784$	4.69473	−	5.19226i	0.167669	−	0.185438i
$785$	28.1099	+	11.5071i	1.00328	+	0.410705i
$786$	−17.2513	+	3.66687i	−0.615332	+	0.130793i
$787$	−12.9392	−	19.9247i	−0.461234	−	0.710239i	0.529158	−	0.848523i	$-0.322508\pi$
$787$	−12.9392	−	19.9247i	−0.461234	−	0.710239i	−0.990393	+	0.138285i	$0.955841\pi$
$788$	−0.984469	−	1.51595i	−0.0350702	−	0.0540034i
$789$	29.6415	−	6.30050i	1.05527	−	0.224304i
$790$	−25.8623	+	6.32261i	−0.920138	+	0.224948i
$791$	−13.0790	−	6.68125i	−0.465037	−	0.237558i
$792$	1.20671	−	7.61884i	0.0428784	−	0.270724i
$793$	−3.21326	+	11.9920i	−0.114106	+	0.425850i
$794$	−2.82806	−	26.9072i	−0.100364	−	0.954899i
$795$	−47.5253	+	9.01246i	−1.68555	+	0.319639i
$796$	−8.05772	−	0.846900i	−0.285598	−	0.0300176i
$797$	−5.26480	−	33.2406i	−0.186489	−	1.17744i	−0.886298	−	0.463115i	$-0.846732\pi$
$797$	−5.26480	−	33.2406i	−0.186489	−	1.17744i	0.699810	−	0.714329i	$-0.253268\pi$
$798$	−27.1589	+	5.74328i	−0.961415	+	0.203310i
$799$			31.8893i			1.12816i
$800$	4.30923	−	2.53585i	0.152354	−	0.0896560i
$801$	−74.8711	−	43.2268i	−2.64544	−	1.52734i
$802$	20.0643	+	1.05153i	0.708496	+	0.0371307i
$803$	−11.0081	−	13.5938i	−0.388466	−	0.479716i
$804$	−13.9427	−	10.1300i	−0.491723	−	0.357257i
$805$	26.6198	−	9.51983i	0.938225	−	0.335530i
$806$	−18.9850	+	13.7934i	−0.668717	+	0.485851i
$807$	−4.29135	−	1.14986i	−0.151063	−	0.0404771i
$808$	14.5473	+	11.7802i	0.511772	+	0.414424i
$809$	−5.87133	+	27.6224i	−0.206425	+	0.971154i	0.745898	+	0.666061i	$0.232021\pi$
$809$	−5.87133	+	27.6224i	−0.206425	+	0.971154i	−0.952323	+	0.305093i	$0.901313\pi$
$810$	23.0458	+	47.8049i	0.809746	+	1.67969i
$811$	−46.3118	−	15.0476i	−1.62623	−	0.528393i	−0.652826	−	0.757508i	$-0.726417\pi$
$811$	−46.3118	−	15.0476i	−1.62623	−	0.528393i	−0.973399	+	0.229115i	$0.926417\pi$
$812$	2.79266	−	13.0715i	0.0980030	−	0.458721i
$813$	−13.3714	+	26.2429i	−0.468957	+	0.920380i
$814$	−0.550088	−	2.58796i	−0.0192806	−	0.0907080i
$815$	−18.8235	−	12.8224i	−0.659359	−	0.449147i
$816$	−8.55842	−	1.81915i	−0.299605	−	0.0636829i
$817$	8.11840	+	21.1492i	0.284027	+	0.739915i
$818$	−20.7700	+	20.7700i	−0.726205	+	0.726205i
$819$	−81.7365	+	31.2782i	−2.85610	+	1.09295i
$820$	0.333466	+	4.02354i	0.0116451	+	0.140508i
$821$	0.107744	−	1.02512i	0.00376029	−	0.0357768i	−0.992481	−	0.122400i	$-0.960941\pi$
$821$	0.107744	−	1.02512i	0.00376029	−	0.0357768i	0.996241	+	0.0866232i	$0.0276076\pi$
$822$	44.1533	+	16.9489i	1.54002	+	0.591159i
$823$	−0.574771	+	10.9673i	−0.0200353	+	0.382295i	0.970147	+	0.242516i	$0.0779727\pi$
$823$	−0.574771	+	10.9673i	−0.0200353	+	0.382295i	−0.990183	+	0.139779i	$0.955361\pi$
$824$	8.12796	+	14.0780i	0.283151	+	0.490432i
$825$	−9.97944	−	13.4985i	−0.347440	−	0.469957i
$826$	25.2357	+	25.2883i	0.878063	+	0.879892i
$827$	−2.74824	−	5.39372i	−0.0955656	−	0.187558i	0.838275	−	0.545248i	$-0.183564\pi$
$827$	−2.74824	−	5.39372i	−0.0955656	−	0.187558i	−0.933840	+	0.357690i	$0.883564\pi$
$828$	−27.5360	+	22.2982i	−0.956942	+	0.774916i
$829$	5.23637	−	2.33138i	0.181867	−	0.0809723i	−0.313783	−	0.949495i	$-0.601597\pi$
$829$	5.23637	−	2.33138i	0.181867	−	0.0809723i	0.495650	+	0.868522i	$0.334930\pi$
$830$	−1.45840	−	7.69055i	−0.0506217	−	0.266943i
$831$	14.9628	−	33.6069i	0.519052	−	1.16581i
$832$	−3.15452	−	3.15452i	−0.109363	−	0.109363i
$833$	−11.9743	+	14.7243i	−0.414884	+	0.510165i
$834$	35.1614	−	11.4246i	1.21754	−	0.395603i
$835$	11.2868	+	11.7954i	0.390596	+	0.408197i
$836$	−2.51356	+	2.26322i	−0.0869333	+	0.0782751i
$837$	−62.8519	+	40.8165i	−2.17248	+	1.41082i
$838$	0.625910	+	11.9431i	0.0216217	+	0.412567i
$839$	0.387312	−	1.19202i	0.0133715	−	0.0411533i	−0.944148	−	0.329521i	$-0.893113\pi$
$839$	0.387312	−	1.19202i	0.0133715	−	0.0411533i	0.957520	+	0.288368i	$0.0931127\pi$
$840$	7.36111	+	17.6161i	0.253982	+	0.607815i
$841$	1.07432	+	3.30643i	0.0370456	+	0.114015i
$842$	11.3732	−	4.36575i	0.391946	−	0.150454i
$843$	21.1115	+	78.7892i	0.727118	+	2.71364i
$844$	4.22637	−	0.444210i	0.145478	−	0.0152903i
$845$	0.339970	−	15.4297i	0.0116953	−	0.530798i
$846$	−51.2615	+	70.5554i	−1.76241	+	2.42574i
$847$	26.0931	+	2.76995i	0.896570	+	0.0951765i
$848$	5.97268	−	3.04323i	0.205103	−	0.104505i
$849$	10.1194	−	5.84244i	0.347297	−	0.200512i
$850$	−11.3075	+	7.47731i	−0.387843	+	0.256470i
$851$	−6.07648	+	10.5248i	−0.208299	+	0.360785i
$852$	21.4009	+	13.8979i	0.733182	+	0.476134i
$853$	−21.7952	+	3.45202i	−0.746253	+	0.118195i	−0.517969	−	0.855400i	$-0.673312\pi$
$853$	−21.7952	+	3.45202i	−0.746253	+	0.118195i	−0.228285	+	0.973594i	$0.573312\pi$
$854$	−2.64578	+	6.87111i	−0.0905367	+	0.235125i
$855$	12.3659	−	52.4661i	0.422906	−	1.79430i
$856$	3.32318	+	1.47958i	0.113584	+	0.0505709i
$857$	23.5265	−	6.30391i	0.803650	−	0.215337i	0.166464	−	0.986048i	$-0.446765\pi$
$857$	23.5265	−	6.30391i	0.803650	−	0.215337i	0.637186	+	0.770710i	$0.280098\pi$
$858$	−9.42584	+	11.6399i	−0.321793	+	0.397381i
$859$	−4.72494	+	5.24757i	−0.161213	+	0.179045i	−0.818339	−	0.574735i	$-0.805105\pi$
$859$	−4.72494	+	5.24757i	−0.161213	+	0.179045i	0.657127	+	0.753780i	$0.271772\pi$
$860$	13.2508	−	8.19594i	0.451849	−	0.279479i
$861$	−15.3944	−	0.822845i	−0.524639	−	0.0280425i
$862$	−28.4141	−	14.4777i	−0.967788	−	0.493113i
$863$	0.785128	−	0.0411468i	0.0267261	−	0.00140065i	−0.0389682	−	0.999240i	$-0.512407\pi$
$863$	0.785128	−	0.0411468i	0.0267261	−	0.00140065i	0.0656943	+	0.997840i	$0.479074\pi$
$864$	−9.53311	−	10.5876i	−0.324323	−	0.360197i
$865$	−4.03006	+	1.44597i	−0.137026	+	0.0491644i
$866$	5.01149	+	4.51237i	0.170297	+	0.153337i
$867$	−30.7565	−	4.87135i	−1.04454	−	0.165440i
$868$	−12.0599	+	6.94606i	−0.409339	+	0.235765i
$869$	−7.28084	−	10.0212i	−0.246985	−	0.339946i
$870$	29.0149	+	22.0732i	0.983698	+	0.748352i
$871$	9.69013	+	21.7644i	0.328338	+	0.737458i
$872$	−1.43151	+	3.72920i	−0.0484769	+	0.126287i
$873$	22.6774	−	34.9202i	0.767515	−	1.18187i
$874$	15.5362			0.525520
$875$	27.4561	+	11.0074i	0.928186	+	0.372117i
$876$	−54.2608			−1.83330
$877$	6.99286	−	10.7681i	0.236132	−	0.363612i	−0.700662	−	0.713494i	$-0.747112\pi$
$877$	6.99286	−	10.7681i	0.236132	−	0.363612i	0.936794	+	0.349882i	$0.113778\pi$
$878$	−3.54466	+	9.23416i	−0.119627	+	0.311638i
$879$	−27.7222	−	62.2651i	−0.935046	−	2.10015i
$880$	1.85142	+	1.40847i	0.0624113	+	0.0474797i
$881$	8.48452	+	11.6779i	0.285851	+	0.393440i	0.927661	−	0.373424i	$-0.121816\pi$
$881$	8.48452	+	11.6779i	0.285851	+	0.393440i	−0.641810	+	0.766864i	$0.721816\pi$
$882$	−50.1621	+	13.3291i	−1.68905	+	0.448814i
$883$	−32.2573	−	5.10905i	−1.08554	−	0.171933i	−0.412076	−	0.911150i	$-0.635196\pi$
$883$	−32.2573	−	5.10905i	−1.08554	−	0.171933i	−0.673468	+	0.739216i	$0.735196\pi$
$884$	8.98852	+	8.09330i	0.302317	+	0.272207i
$885$	−91.7163	+	32.9074i	−3.08301	+	1.10617i
$886$	−12.8775	−	14.3019i	−0.432627	−	0.480481i
$887$	−35.0007	+	1.83431i	−1.17521	+	0.0615902i	−0.629922	−	0.776658i	$-0.716913\pi$
$887$	−35.0007	+	1.83431i	−1.17521	+	0.0615902i	−0.545288	+	0.838249i	$0.683580\pi$
$888$	−7.31277	−	3.72604i	−0.245400	−	0.125038i
$889$	−20.7886	+	10.5651i	−0.697228	+	0.354342i
$890$	22.1733	−	13.7147i	0.743252	−	0.459719i
$891$	−16.5215	+	18.3490i	−0.553492	+	0.614716i
$892$	13.6129	−	16.8105i	0.455794	−	0.562859i
$893$	36.9371	−	9.89727i	1.23605	−	0.331200i
$894$	21.2283	+	9.45147i	0.709982	+	0.316104i
$895$	−5.75484	+	24.4166i	−0.192363	+	0.816157i
$896$	−1.66289	−	2.05787i	−0.0555531	−	0.0687485i
$897$	67.9512	−	10.7624i	2.26882	−	0.359346i
$898$	−10.0946	−	6.55551i	−0.336861	−	0.218760i
$899$	−13.2875	+	23.0146i	−0.443162	+	0.767579i
$900$	−37.0375	−	1.63292i	−1.23458	−	0.0544307i
$901$	−15.7393	+	9.08708i	−0.524352	+	0.302735i
$902$	−1.67366	+	0.852771i	−0.0557267	+	0.0283942i
$903$	24.1419	+	54.3756i	0.803390	+	1.80951i
$904$	−3.26283	+	4.49090i	−0.108520	+	0.149365i
$905$	0.121739	−	5.52521i	0.00404676	−	0.183664i
$906$	17.4584	−	1.83495i	0.580017	−	0.0609623i
$907$	−2.69653	−	10.0636i	−0.0895367	−	0.334155i	0.906598	−	0.421996i	$-0.138670\pi$
$907$	−2.69653	−	10.0636i	−0.0895367	−	0.334155i	−0.996135	+	0.0878401i	$0.972004\pi$
$908$	−1.98976	+	0.763797i	−0.0660324	+	0.0253475i
$909$	−42.8899	−	132.001i	−1.42257	−	4.37821i
$910$	3.36354	−	26.1774i	0.111500	−	0.867774i
$911$	−6.09412	+	18.7558i	−0.201907	+	0.621407i	0.797919	+	0.602765i	$0.205934\pi$
$911$	−6.09412	+	18.7558i	−0.201907	+	0.621407i	−0.999826	+	0.0186419i	$0.994066\pi$
$912$	0.549115	+	10.4777i	0.0181830	+	0.346953i
$913$	3.05430	−	1.98349i	0.101083	−	0.0656438i
$914$	22.1529	−	19.9465i	0.732752	−	0.659773i
$915$	−13.8839	−	14.5095i	−0.458988	−	0.479670i
$916$	28.5588	−	9.27930i	0.943608	−	0.306597i
$917$	13.2029	+	5.89480i	0.436000	+	0.194663i
$918$	27.3133	+	27.3133i	0.901474	+	0.901474i
$919$	−15.6091	+	35.0585i	−0.514895	+	1.15647i	0.449806	+	0.893126i	$0.351493\pi$
$919$	−15.6091	+	35.0585i	−0.514895	+	1.15647i	−0.964701	+	0.263347i	$0.915174\pi$
$920$	−1.99084	−	10.4983i	−0.0656361	−	0.346118i
$921$	34.3050	−	15.2736i	1.13039	−	0.503282i
$922$	1.22009	−	0.988009i	0.0401815	−	0.0325383i
$923$	−16.0145	−	31.4302i	−0.527123	−	1.03454i
$924$	−6.28760	+	6.27453i	−0.206847	+	0.206417i
$925$	−12.0605	+	4.02967i	−0.396548	+	0.132495i
$926$	9.16833	+	15.8800i	0.301290	+	0.521850i
$927$	6.30819	−	120.367i	0.207188	−	3.95339i
$928$	−4.71651	−	1.81050i	−0.154827	−	0.0594326i
$929$	3.90243	−	37.1291i	0.128034	−	1.21817i	−0.722170	−	0.691715i	$-0.756855\pi$
$929$	3.90243	−	37.1291i	0.128034	−	1.21817i	0.850205	−	0.526452i	$-0.176478\pi$
$930$	−3.13522	−	37.8290i	−0.102808	−	1.24046i
$931$	20.7714	+	9.29983i	0.680754	+	0.304790i
$932$	−2.05258	+	2.05258i	−0.0672346	+	0.0672346i
$933$	−2.80203	−	7.29954i	−0.0917344	−	0.238976i
$934$	8.80206	+	1.87093i	0.288012	+	0.0612189i
$935$	−5.21259	−	3.55076i	−0.170470	−	0.116122i
$936$	6.87735	+	32.3554i	0.224793	+	1.05757i
$937$	−5.75516	+	11.2951i	−0.188013	+	0.368996i	−0.965702	−	0.259653i	$-0.916392\pi$
$937$	−5.75516	+	11.2951i	−0.188013	+	0.368996i	0.777689	+	0.628649i	$0.216392\pi$
$938$	4.35217	+	13.4422i	0.142103	+	0.438902i
$939$	−72.4389	−	23.5368i	−2.36395	−	0.768095i
$940$	−11.4211	−	23.6913i	−0.372515	−	0.772724i
$941$	−3.46369	+	16.2954i	−0.112913	+	0.531215i	0.884939	+	0.465707i	$0.154200\pi$
$941$	−3.46369	+	16.2954i	−0.112913	+	0.531215i	−0.997852	+	0.0655075i	$0.979133\pi$
$942$	34.0677	+	27.5875i	1.10998	+	0.898848i
$943$	8.33409	+	2.23311i	0.271395	+	0.0727201i
$944$	10.9242	−	7.93693i	0.355554	−	0.258325i
$945$	15.1022	−	82.9224i	0.491274	−	2.69747i
$946$	5.86455	+	4.26085i	0.190673	+	0.138532i
$947$	−12.2865	−	15.1725i	−0.399257	−	0.493041i	0.537381	−	0.843339i	$-0.319414\pi$
$947$	−12.2865	−	15.1725i	−0.399257	−	0.493041i	−0.936638	+	0.350298i	$0.886080\pi$
$948$	−38.3720	−	2.01099i	−1.24626	−	0.0653139i
$949$	64.9595	+	37.5044i	2.10868	+	1.21744i
$950$	12.1703	+	10.7767i	0.394858	+	0.349641i
$951$			68.2377i			2.21276i
$952$	4.79428	+	5.33574i	0.155384	+	0.172932i
$953$	1.00435	+	6.34121i	0.0325340	+	0.205412i	0.998601	−	0.0528805i	$-0.0168402\pi$
$953$	1.00435	+	6.34121i	0.0325340	+	0.205412i	−0.966067	+	0.258292i	$0.916840\pi$
$954$	−49.4306	−	5.19537i	−1.60038	−	0.168206i
$955$	20.5805	−	3.90278i	0.665968	−	0.126291i
$956$	0.596147	+	5.67196i	0.0192808	+	0.183444i
$957$	−4.39000	+	16.3837i	−0.141909	+	0.529610i
$958$	−2.45172	+	15.4795i	−0.0792115	+	0.500122i
$959$	−21.0838	−	32.5403i	−0.680832	−	1.05078i
$960$	7.00976	−	1.71369i	0.226239	−	0.0553092i
$961$	−3.25743	+	0.692388i	−0.105078	+	0.0223351i
$962$	6.17924	+	9.51520i	0.199227	+	0.306782i
$963$	−14.6901	−	22.6208i	−0.473383	−	0.728946i
$964$	−8.17367	+	1.73737i	−0.263256	+	0.0559568i
$965$	−25.3331	−	10.3704i	−0.815502	−	0.333834i
$966$	40.7479	−	2.09300i	1.31104	−	0.0673412i
$967$	−1.93475	+	12.2156i	−0.0622175	+	0.392826i	0.936853	+	0.349723i	$0.113724\pi$
$967$	−1.93475	+	12.2156i	−0.0622175	+	0.392826i	−0.999071	+	0.0431028i	$0.986276\pi$
$968$	2.56689	−	9.57975i	0.0825029	−	0.307905i
$969$	−2.97347	−	28.2907i	−0.0955217	−	0.908828i
$970$	6.03730	+	11.0101i	0.193846	+	0.353514i
$971$	9.85185	+	1.03547i	0.316161	+	0.0332298i	0.261280	−	0.965263i	$-0.415855\pi$
$971$	9.85185	+	1.03547i	0.316161	+	0.0332298i	0.0548809	+	0.998493i	$0.482522\pi$
$972$	5.29555	+	33.4348i	0.169855	+	1.07242i
$973$	−28.8168	−	9.39629i	−0.923823	−	0.301231i
$974$		−	11.1906i		−	0.358570i
$975$	60.6951	+	38.7034i	1.94380	+	1.23950i
$976$	2.41008	+	1.39146i	0.0771447	+	0.0445395i
$977$	20.5478	+	1.07686i	0.657382	+	0.0344519i	0.378111	−	0.925760i	$-0.376574\pi$
$977$	20.5478	+	1.07686i	0.657382	+	0.0344519i	0.279271	+	0.960212i	$0.409907\pi$
$978$	−20.6864	−	25.5455i	−0.661477	−	0.816856i
$979$	9.81350	+	7.12992i	0.313641	+	0.227873i
$980$	3.62249	−	15.2275i	0.115716	−	0.486425i
$981$	23.9615	−	17.4091i	0.765033	−	0.555829i
$982$	−39.6399	−	10.6215i	−1.26496	−	0.338945i
$983$	3.86240	+	3.12771i	0.123191	+	0.0997584i	0.688936	−	0.724822i	$-0.258078\pi$
$983$	3.86240	+	3.12771i	0.123191	+	0.0997584i	−0.565745	+	0.824580i	$0.691411\pi$
$984$	−1.21147	+	5.69950i	−0.0386202	+	0.181694i
$985$	−3.56000	−	1.91384i	−0.113431	−	0.0609799i
$986$	13.0269	+	4.23270i	0.414862	+	0.134797i
$987$	95.5442	−	30.9344i	3.04121	−	0.984651i
$988$	6.58470	−	12.9232i	0.209487	−	0.411142i
$989$	−6.92285	−	32.5694i	−0.220134	−	1.03565i
$990$	−5.82513	−	16.2352i	−0.185135	−	0.515989i
$991$	−32.1318	−	6.82984i	−1.02070	−	0.216957i	−0.332982	−	0.942933i	$-0.608055\pi$
$991$	−32.1318	−	6.82984i	−1.02070	−	0.216957i	−0.687720	+	0.725976i	$0.741388\pi$
$992$	1.88509	+	4.91083i	0.0598517	+	0.155919i
$993$	21.4485	−	21.4485i	0.680647	−	0.680647i
$994$	−7.47681	−	19.5385i	−0.237150	−	0.619723i
$995$	−16.7089	+	7.00242i	−0.529707	+	0.221992i
$996$	1.18087	−	11.2352i	0.0374173	−	0.356002i
$997$	11.0241	+	4.23174i	0.349135	+	0.134021i	0.526615	−	0.850104i	$-0.323461\pi$
$997$	11.0241	+	4.23174i	0.349135	+	0.134021i	−0.177479	+	0.984125i	$0.556794\pi$
$998$	0.672493	−	12.8319i	0.0212874	−	0.406187i
$999$	18.1164	+	31.3785i	0.573177	+	0.992771i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.x.a.3.1	✓	320
7.5	odd	6	inner	350.2.x.a.103.20	yes	320
25.17	odd	20	inner	350.2.x.a.17.20	yes	320
175.117	even	60	inner	350.2.x.a.117.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.x.a.3.1	✓	320	1.1	even	1	trivial
350.2.x.a.17.20	yes	320	25.17	odd	20	inner
350.2.x.a.103.20	yes	320	7.5	odd	6	inner
350.2.x.a.117.1	yes	320	175.117	even	60	inner

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.544639 + 0.838671i) q^{2} +(-1.15652 + 3.01283i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.77963 - 1.35386i) q^{5} +(-1.89689 - 2.61084i) q^{6} +(-0.00275235 + 2.64575i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-5.51019 - 4.96140i) q^{9} +(2.10469 - 0.755156i) q^{10} +(0.696124 + 0.773125i) q^{11} +(3.22276 - 0.168898i) q^{12} +(-3.97493 - 2.02533i) q^{13} +(-2.21741 - 1.44329i) q^{14} +(6.13712 - 3.79595i) q^{15} +(-0.669131 + 0.743145i) q^{16} +(1.70623 - 2.10702i) q^{17} +(7.16204 - 1.91906i) q^{18} +(-2.97009 - 1.32237i) q^{19} +(-0.512972 + 2.17643i) q^{20} +(-7.96802 - 3.06815i) q^{21} +(-1.02753 + 0.162745i) q^{22} +(4.00771 + 2.60264i) q^{23} +(-1.61359 + 2.79482i) q^{24} +(1.33414 + 4.81872i) q^{25} +(3.86349 - 2.23059i) q^{26} +(12.6942 - 6.46801i) q^{27} +(2.41813 - 1.07361i) q^{28} +(2.96953 - 4.08721i) q^{29} +(-0.158959 + 7.21444i) q^{30} +(-5.23139 + 0.549842i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-3.13438 + 1.20317i) q^{33} +(0.837815 + 2.57853i) q^{34} +(3.58687 - 4.70472i) q^{35} +(-2.29127 + 7.05179i) q^{36} +(0.133100 + 2.53970i) q^{37} +(2.72666 - 1.77072i) q^{38} +(10.6991 - 9.63348i) q^{39} +(-1.54593 - 1.61558i) q^{40} +(1.71718 - 0.557946i) q^{41} +(6.91286 - 5.01151i) q^{42} +(-4.92704 - 4.92704i) q^{43} +(0.423145 - 0.950399i) q^{44} +(3.08905 + 16.2894i) q^{45} +(-4.36551 + 1.94365i) q^{46} +(-9.14075 + 7.40204i) q^{47} +(-1.46511 - 2.87544i) q^{48} +(-6.99998 - 0.0145640i) q^{49} +(-4.76794 - 1.50556i) q^{50} +(4.37481 + 7.57739i) q^{51} +(-0.233480 + 4.45506i) q^{52} +(-6.25807 - 2.40225i) q^{53} +(-1.48922 + 14.1690i) q^{54} +(-0.192140 - 2.31833i) q^{55} +(-0.416605 + 2.61275i) q^{56} +(7.41905 - 7.41905i) q^{57} +(1.81050 + 4.71651i) q^{58} +(-13.2080 - 2.80746i) q^{59} +(-5.96397 - 4.06258i) q^{60} +(-0.578601 - 2.72210i) q^{61} +(2.38808 - 4.68688i) q^{62} +(13.1418 - 14.5649i) q^{63} +(0.951057 + 0.309017i) q^{64} +(4.33188 + 8.98582i) q^{65} +(0.698037 - 3.28400i) q^{66} +(-4.15021 - 3.36077i) q^{67} +(-2.61884 - 0.701717i) q^{68} +(-12.4763 + 9.06456i) q^{69} +(1.99216 + 5.57057i) q^{70} +(6.39697 + 4.64767i) q^{71} +(-4.66622 - 5.76230i) q^{72} +(-16.7907 - 0.879961i) q^{73} +(-2.20246 - 1.27159i) q^{74} +(-16.0610 - 1.55341i) q^{75} +3.25117i q^{76} +(-2.04741 + 1.83964i) q^{77} +(2.25219 + 14.2198i) q^{78} +(-11.8413 - 1.24458i) q^{79} +(2.19691 - 0.416612i) q^{80} +(2.48084 + 23.6036i) q^{81} +(-0.467311 + 1.74403i) q^{82} +(0.547617 - 3.45752i) q^{83} +(0.437991 + 8.52708i) q^{84} +(-5.88906 + 1.43971i) q^{85} +(6.81562 - 1.44871i) q^{86} +(8.87976 + 13.6736i) q^{87} +(0.566611 + 0.872504i) q^{88} +(11.4050 - 2.42420i) q^{89} +(-15.3439 - 6.28118i) q^{90} +(5.36946 - 10.5111i) q^{91} +(0.747545 - 4.71981i) q^{92} +(4.39362 - 16.3972i) q^{93} +(-1.22946 - 11.6975i) q^{94} +(3.49535 + 6.37441i) q^{95} +(3.20950 + 0.337332i) q^{96} +(0.878465 + 5.54641i) q^{97} +(3.82468 - 5.86275i) q^{98} -7.71381i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37}+ \cdots - 40 q^{98}+O(q^{100}) \) 320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more