LMFDB - Embedded newform 273.2.cc.a.50.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.19
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.790296 + 0.211759i) q^{2} +(1.66735 + 0.468978i) q^{3} +(-1.15232 - 0.665295i) q^{4} +(2.01842 - 2.01842i) q^{5} +(1.21839 + 0.723709i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-1.92687 - 1.92687i) q^{8} +(2.56012 + 1.56390i) q^{9} +O(q^{10})$	\(q+(0.790296 + 0.211759i) q^{2} +(1.66735 + 0.468978i) q^{3} +(-1.15232 - 0.665295i) q^{4} +(2.01842 - 2.01842i) q^{5} +(1.21839 + 0.723709i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-1.92687 - 1.92687i) q^{8} +(2.56012 + 1.56390i) q^{9} +(2.02257 - 1.16773i) q^{10} +(-1.07945 + 4.02854i) q^{11} +(-1.60932 - 1.64970i) q^{12} +(1.07061 - 3.44294i) q^{13} -0.818175i q^{14} +(4.31201 - 2.41882i) q^{15} +(0.215825 + 0.373820i) q^{16} +(-0.779536 + 1.35020i) q^{17} +(1.69208 + 1.77808i) q^{18} +(-4.81947 + 1.29137i) q^{19} +(-3.66872 + 0.983030i) q^{20} +(0.0214561 - 1.73192i) q^{21} +(-1.70616 + 2.95516i) q^{22} +(3.08448 + 5.34248i) q^{23} +(-2.30911 - 4.11643i) q^{24} -3.14802i q^{25} +(1.57517 - 2.49423i) q^{26} +(3.53518 + 3.80822i) q^{27} +(-0.344382 + 1.28525i) q^{28} +(0.174124 - 0.100531i) q^{29} +(3.91997 - 0.998475i) q^{30} +(4.04028 + 4.04028i) q^{31} +(1.50197 + 5.60544i) q^{32} +(-3.68911 + 6.21076i) q^{33} +(-0.901981 + 0.901981i) q^{34} +(-2.47205 - 1.42724i) q^{35} +(-1.90963 - 3.50536i) q^{36} +(-10.1313 - 2.71468i) q^{37} -4.08227 q^{38} +(3.39974 - 5.23849i) q^{39} -7.77846 q^{40} +(3.01738 + 0.808505i) q^{41} +(0.383706 - 1.36418i) q^{42} +(-7.70910 - 4.45085i) q^{43} +(3.92404 - 3.92404i) q^{44} +(8.32400 - 2.01078i) q^{45} +(1.30634 + 4.87531i) q^{46} +(-2.13415 - 2.13415i) q^{47} +(0.184543 + 0.724506i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.666623 - 2.48787i) q^{50} +(-1.93297 + 1.88567i) q^{51} +(-3.52425 + 3.25511i) q^{52} -3.59796i q^{53} +(1.98741 + 3.75822i) q^{54} +(5.95252 + 10.3101i) q^{55} +(-1.36250 + 2.35992i) q^{56} +(-8.64138 - 0.107055i) q^{57} +(0.158898 - 0.0425766i) q^{58} +(1.31999 - 0.353691i) q^{59} +(-6.57806 - 0.0814933i) q^{60} +(6.08621 - 10.5416i) q^{61} +(2.33745 + 4.04859i) q^{62} +(0.848007 - 2.87765i) q^{63} +3.88471i q^{64} +(-4.78835 - 9.11021i) q^{65} +(-4.23068 + 4.12714i) q^{66} +(1.31959 - 4.92478i) q^{67} +(1.79656 - 1.03724i) q^{68} +(2.63741 + 10.3543i) q^{69} +(-1.65142 - 1.65142i) q^{70} +(-0.799966 - 2.98551i) q^{71} +(-1.91958 - 7.94645i) q^{72} +(-10.2930 + 10.2930i) q^{73} +(-7.43189 - 4.29080i) q^{74} +(1.47636 - 5.24886i) q^{75} +(6.41274 + 1.71829i) q^{76} +4.17066 q^{77} +(3.79610 - 3.42003i) q^{78} +1.20273 q^{79} +(1.19015 + 0.318900i) q^{80} +(4.10841 + 8.00755i) q^{81} +(2.21342 + 1.27792i) q^{82} +(-3.18309 + 3.18309i) q^{83} +(-1.17696 + 1.98146i) q^{84} +(1.15183 + 4.29869i) q^{85} +(-5.14996 - 5.14996i) q^{86} +(0.337473 - 0.0859595i) q^{87} +(9.84243 - 5.68253i) q^{88} +(3.73572 - 13.9419i) q^{89} +(7.00423 + 0.173573i) q^{90} +(-3.60271 - 0.143028i) q^{91} -8.20837i q^{92} +(4.84177 + 8.63138i) q^{93} +(-1.23468 - 2.13853i) q^{94} +(-7.12118 + 12.3342i) q^{95} +(-0.124514 + 10.0506i) q^{96} +(-1.79851 + 0.481910i) q^{97} +(-0.790296 + 0.211759i) q^{98} +(-9.06376 + 8.62540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.790296	+	0.211759i	0.558824	+	0.149736i	0.527166	−	0.849762i	$-0.323255\pi$
$2$	0.790296	+	0.211759i	0.558824	+	0.149736i	0.0316579	+	0.999499i	$0.489921\pi$
$3$	1.66735	+	0.468978i	0.962646	+	0.270765i
$3$	1.66735	+	0.468978i	0.962646	+	0.270765i
$4$	−1.15232	−	0.665295i	−0.576162	−	0.332648i
$5$	2.01842	−	2.01842i	0.902664	−	0.902664i	−0.0930018	−	0.995666i	$-0.529646\pi$
$5$	2.01842	−	2.01842i	0.902664	−	0.902664i	0.995666	+	0.0930018i	$0.0296462\pi$
$6$	1.21839	+	0.723709i	0.497406	+	0.295453i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$8$	−1.92687	−	1.92687i	−0.681251	−	0.681251i
$9$	2.56012	+	1.56390i	0.853373	+	0.521301i
$10$	2.02257	−	1.16773i	0.639592	−	0.369269i
$11$	−1.07945	+	4.02854i	−0.325465	+	1.21465i	0.588379	+	0.808586i	$0.299766\pi$
$11$	−1.07945	+	4.02854i	−0.325465	+	1.21465i	−0.913844	+	0.406066i	$0.866900\pi$
$12$	−1.60932	−	1.64970i	−0.464571	−	0.476226i
$13$	1.07061	−	3.44294i	0.296933	−	0.954898i
$13$	1.07061	−	3.44294i	0.296933	−	0.954898i
$14$		−	0.818175i		−	0.218666i
$15$	4.31201	−	2.41882i	1.11336	−	0.624536i
$16$	0.215825	+	0.373820i	0.0539562	+	0.0934549i
$17$	−0.779536	+	1.35020i	−0.189065	+	0.327471i	−0.944939	−	0.327247i	$-0.893879\pi$
$17$	−0.779536	+	1.35020i	−0.189065	+	0.327471i	0.755874	+	0.654718i	$0.227212\pi$
$18$	1.69208	+	1.77808i	0.398827	+	0.419096i
$19$	−4.81947	+	1.29137i	−1.10566	+	0.296261i	−0.765068	−	0.643949i	$-0.777295\pi$
$19$	−4.81947	+	1.29137i	−1.10566	+	0.296261i	−0.340594	+	0.940210i	$0.610628\pi$
$20$	−3.66872	+	0.983030i	−0.820350	+	0.219812i
$21$	0.0214561	−	1.73192i	0.00468211	−	0.377935i
$22$	−1.70616	+	2.95516i	−0.363755	+	0.630042i
$23$	3.08448	+	5.34248i	0.643159	+	1.11398i	0.984723	+	0.174126i	$0.0557100\pi$
$23$	3.08448	+	5.34248i	0.643159	+	1.11398i	−0.341564	+	0.939858i	$0.610957\pi$
$24$	−2.30911	−	4.11643i	−0.471345	−	0.840262i
$25$		−	3.14802i		−	0.629605i
$26$	1.57517	−	2.49423i	0.308916	−	0.489158i
$27$	3.53518	+	3.80822i	0.680346	+	0.732891i
$28$	−0.344382	+	1.28525i	−0.0650821	+	0.242890i
$29$	0.174124	−	0.100531i	0.0323341	−	0.0186681i	−0.483746	−	0.875209i	$-0.660724\pi$
$29$	0.174124	−	0.100531i	0.0323341	−	0.0186681i	0.516080	+	0.856540i	$0.327391\pi$
$30$	3.91997	−	0.998475i	0.715685	−	0.182296i
$31$	4.04028	+	4.04028i	0.725657	+	0.725657i	0.969751	−	0.244095i	$-0.0784908\pi$
$31$	4.04028	+	4.04028i	0.725657	+	0.725657i	−0.244095	+	0.969751i	$0.578491\pi$
$32$	1.50197	+	5.60544i	0.265514	+	0.990910i
$33$	−3.68911	+	6.21076i	−0.642192	+	1.08115i
$34$	−0.901981	+	0.901981i	−0.154688	+	0.154688i
$35$	−2.47205	−	1.42724i	−0.417852	−	0.241247i
$36$	−1.90963	−	3.50536i	−0.318272	−	0.584226i
$37$	−10.1313	−	2.71468i	−1.66558	−	0.446291i	−0.701666	−	0.712506i	$-0.747560\pi$
$37$	−10.1313	−	2.71468i	−1.66558	−	0.446291i	−0.963914	+	0.266215i	$0.914227\pi$
$38$	−4.08227			−0.662232
$39$	3.39974	−	5.23849i	0.544394	−	0.838830i
$40$	−7.77846			−1.22988
$41$	3.01738	+	0.808505i	0.471236	+	0.126267i	0.486619	−	0.873614i	$-0.338230\pi$
$41$	3.01738	+	0.808505i	0.471236	+	0.126267i	−0.0153831	+	0.999882i	$0.504897\pi$
$42$	0.383706	−	1.36418i	0.0592072	−	0.210498i
$43$	−7.70910	−	4.45085i	−1.17563	−	0.678748i	−0.220628	−	0.975358i	$-0.570811\pi$
$43$	−7.70910	−	4.45085i	−1.17563	−	0.678748i	−0.954999	+	0.296610i	$0.904144\pi$
$44$	3.92404	−	3.92404i	0.591572	−	0.591572i
$45$	8.32400	−	2.01078i	1.24087	−	0.299749i
$46$	1.30634	+	4.87531i	0.192609	+	0.718825i
$47$	−2.13415	−	2.13415i	−0.311297	−	0.311297i	0.534115	−	0.845412i	$-0.320645\pi$
$47$	−2.13415	−	2.13415i	−0.311297	−	0.311297i	−0.845412	+	0.534115i	$0.820645\pi$
$48$	0.184543	+	0.724506i	0.0266364	+	0.104573i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	0.666623	−	2.48787i	0.0942748	−	0.351838i
$51$	−1.93297	+	1.88567i	−0.270670	+	0.264046i
$52$	−3.52425	+	3.25511i	−0.488726	+	0.451403i
$53$		−	3.59796i		−	0.494218i	−0.968988	−	0.247109i	$-0.920519\pi$
$53$		−	3.59796i		−	0.494218i	0.968988	−	0.247109i	$-0.0794806\pi$
$54$	1.98741	+	3.75822i	0.270453	+	0.511430i
$55$	5.95252	+	10.3101i	0.802637	+	1.39021i
$56$	−1.36250	+	2.35992i	−0.182072	+	0.315358i
$57$	−8.64138	−	0.107055i	−1.14458	−	0.0141798i
$58$	0.158898	−	0.0425766i	0.0208644	−	0.00559059i
$59$	1.31999	−	0.353691i	0.171848	−	0.0460466i	−0.171869	−	0.985120i	$-0.554981\pi$
$59$	1.31999	−	0.353691i	0.171848	−	0.0460466i	0.343717	+	0.939073i	$0.388314\pi$
$60$	−6.57806	−	0.0814933i	−0.849224	−	0.0105207i
$61$	6.08621	−	10.5416i	0.779259	−	1.34972i	−0.153110	−	0.988209i	$-0.548929\pi$
$61$	6.08621	−	10.5416i	0.779259	−	1.34972i	0.932369	−	0.361508i	$-0.117738\pi$
$62$	2.33745	+	4.04859i	0.296857	+	0.514171i
$63$	0.848007	−	2.87765i	0.106839	−	0.362550i
$64$			3.88471i			0.485589i
$65$	−4.78835	−	9.11021i	−0.593922	−	1.12998i
$66$	−4.23068	+	4.12714i	−0.520761	+	0.508015i
$67$	1.31959	−	4.92478i	0.161214	−	0.601658i	−0.837279	−	0.546776i	$-0.815855\pi$
$67$	1.31959	−	4.92478i	0.161214	−	0.601658i	0.998493	−	0.0548820i	$-0.0174783\pi$
$68$	1.79656	−	1.03724i	0.217865	−	0.125784i
$69$	2.63741	+	10.3543i	0.317507	+	1.24652i
$70$	−1.65142	−	1.65142i	−0.197382	−	0.197382i
$71$	−0.799966	−	2.98551i	−0.0949385	−	0.354315i	0.902072	−	0.431586i	$-0.142046\pi$
$71$	−0.799966	−	2.98551i	−0.0949385	−	0.354315i	−0.997010	+	0.0772711i	$0.975379\pi$
$72$	−1.91958	−	7.94645i	−0.226224	−	0.936498i
$73$	−10.2930	+	10.2930i	−1.20470	+	1.20470i	−0.231983	+	0.972720i	$0.574521\pi$
$73$	−10.2930	+	10.2930i	−1.20470	+	1.20470i	−0.972720	+	0.231983i	$0.925479\pi$
$74$	−7.43189	−	4.29080i	−0.863940	−	0.498796i
$75$	1.47636	−	5.24886i	0.170475	−	0.606086i
$76$	6.41274	+	1.71829i	0.735592	+	0.197101i
$77$	4.17066			0.475290
$78$	3.79610	−	3.42003i	0.429823	−	0.387243i
$79$	1.20273			0.135318			0.0676591	−	0.997708i	$-0.478447\pi$
$79$	1.20273			0.135318			0.0676591	+	0.997708i	$0.478447\pi$
$80$	1.19015	+	0.318900i	0.133063	+	0.0356541i
$81$	4.10841	+	8.00755i	0.456490	+	0.889728i
$82$	2.21342	+	1.27792i	0.244431	+	0.141122i
$83$	−3.18309	+	3.18309i	−0.349389	+	0.349389i	−0.859882	−	0.510493i	$-0.829463\pi$
$83$	−3.18309	+	3.18309i	−0.349389	+	0.349389i	0.510493	+	0.859882i	$0.329463\pi$
$84$	−1.17696	+	1.98146i	−0.128417	+	0.216195i
$85$	1.15183	+	4.29869i	0.124934	+	0.466258i
$86$	−5.14996	−	5.14996i	−0.555335	−	0.555335i
$87$	0.337473	−	0.0859595i	0.0361809	−	0.00921583i
$88$	9.84243	−	5.68253i	1.04921	−	0.605760i
$89$	3.73572	−	13.9419i	0.395986	−	1.47784i	−0.424109	−	0.905611i	$-0.639413\pi$
$89$	3.73572	−	13.9419i	0.395986	−	1.47784i	0.820095	−	0.572227i	$-0.193921\pi$
$90$	7.00423	+	0.173573i	0.738310	+	0.0182962i
$91$	−3.60271	−	0.143028i	−0.377667	−	0.0149934i
$92$		−	8.20837i		−	0.855781i
$93$	4.84177	+	8.63138i	0.502068	+	0.895032i
$94$	−1.23468	−	2.13853i	−0.127348	−	0.220573i
$95$	−7.12118	+	12.3342i	−0.730617	+	1.26547i
$96$	−0.124514	+	10.0506i	−0.0127081	+	1.02579i
$97$	−1.79851	+	0.481910i	−0.182611	+	0.0489305i	−0.348966	−	0.937135i	$-0.613467\pi$
$97$	−1.79851	+	0.481910i	−0.182611	+	0.0489305i	0.166355	+	0.986066i	$0.446800\pi$
$98$	−0.790296	+	0.211759i	−0.0798320	+	0.0213909i
$99$	−9.06376	+	8.62540i	−0.910942	+	0.866886i
$100$	−2.09437	+	3.62755i	−0.209437	+	0.362755i
$101$	9.30538	+	16.1174i	0.925920	+	1.60374i	0.790075	+	0.613010i	$0.210042\pi$
$101$	9.30538	+	16.1174i	0.925920	+	1.60374i	0.135845	+	0.990730i	$0.456625\pi$
$102$	−1.92693	+	1.08091i	−0.190794	+	0.107026i
$103$		−	0.114296i		−	0.0112620i	−0.999984	−	0.00563098i	$-0.998208\pi$
$103$		−	0.114296i		−	0.0112620i	0.999984	−	0.00563098i	$-0.00179241\pi$
$104$	−8.69700	+	4.57117i	−0.852811	+	0.448240i
$105$	−3.45243	−	3.53904i	−0.336922	−	0.345375i
$106$	0.761901	−	2.84345i	0.0740024	−	0.276181i
$107$	−7.28488	+	4.20593i	−0.704256	+	0.406602i	−0.808931	−	0.587904i	$-0.799953\pi$
$107$	−7.28488	+	4.20593i	−0.704256	+	0.406602i	0.104675	+	0.994507i	$0.466620\pi$
$108$	−1.54009	−	6.74024i	−0.148195	−	0.648580i
$109$	−7.53040	−	7.53040i	−0.721282	−	0.721282i	0.247585	−	0.968866i	$-0.420363\pi$
$109$	−7.53040	−	7.53040i	−0.721282	−	0.721282i	−0.968866	+	0.247585i	$0.920363\pi$
$110$	2.52100	+	9.40850i	0.240368	+	0.897065i
$111$	−15.6194	−	9.27770i	−1.48252	−	0.880600i
$112$	0.305223	−	0.305223i	0.0288408	−	0.0288408i
$113$	5.45610	+	3.15008i	0.513267	+	0.296335i	0.734175	−	0.678960i	$-0.237569\pi$
$113$	5.45610	+	3.15008i	0.513267	+	0.296335i	−0.220909	+	0.975295i	$0.570902\pi$
$114$	−6.80658	−	1.91450i	−0.637494	−	0.179309i
$115$	17.0091	+	4.55759i	1.58611	+	0.424997i
$116$	−0.267531			−0.0248396
$117$	8.12529	−	7.14000i	0.751184	−	0.660093i
$118$	1.11808			0.102928
$119$	1.50595	+	0.403518i	0.138050	+	0.0369904i
$120$	−12.9694	−	3.64793i	−1.18394	−	0.333009i
$121$	−5.53769	−	3.19719i	−0.503426	−	0.290653i
$122$	7.04219	−	7.04219i	0.637570	−	0.637570i
$123$	4.65186	+	2.76315i	0.419444	+	0.249145i
$124$	−1.96774	−	7.34370i	−0.176708	−	0.659484i
$125$	3.73806	+	3.73806i	0.334342	+	0.334342i
$126$	1.27955	−	2.09462i	0.113991	−	0.186604i
$127$	11.8629	−	6.84906i	1.05266	−	0.607756i	0.129270	−	0.991609i	$-0.458737\pi$
$127$	11.8629	−	6.84906i	1.05266	−	0.607756i	0.923394	+	0.383854i	$0.125403\pi$
$128$	2.18132	−	8.14080i	0.192803	−	0.719552i
$129$	−10.7664	−	11.0365i	−0.947930	−	0.971712i
$130$	−1.85505	−	8.21374i	−0.162698	−	0.720393i
$131$			11.0318i			0.963854i	0.876211	+	0.481927i	$0.160063\pi$
$131$			11.0318i			0.963854i	−0.876211	+	0.481927i	$0.839937\pi$
$132$	8.38305	−	4.70246i	0.729651	−	0.409297i
$133$	2.49474	+	4.32102i	0.216322	+	0.374680i
$134$	2.08574	−	3.61260i	0.180180	−	0.312081i
$135$	14.8220	+	0.551101i	1.27568	+	0.0474312i
$136$	4.10372	−	1.09959i	0.351891	−	0.0942888i
$137$	20.9889	−	5.62396i	1.79320	−	0.480487i	0.800318	−	0.599575i	$-0.204664\pi$
$137$	20.9889	−	5.62396i	1.79320	−	0.480487i	0.992884	+	0.119088i	$0.0379972\pi$
$138$	−0.108295	+	8.74150i	−0.00921872	+	0.744126i
$139$	4.42976	−	7.67257i	0.375727	−	0.650779i	−0.614708	−	0.788755i	$-0.710726\pi$
$139$	4.42976	−	7.67257i	0.375727	−	0.650779i	0.990436	+	0.137976i	$0.0440596\pi$
$140$	1.89907	+	3.28928i	0.160501	+	0.277995i
$141$	−2.55750	−	4.55924i	−0.215381	−	0.383957i
$142$		−	2.52884i		−	0.212215i
$143$	12.7144	+	8.02944i	1.06323	+	0.671456i
$144$	−0.0320805	+	1.29455i	−0.00267337	+	0.107879i
$145$	0.148543	−	0.554369i	0.0123358	−	0.0460378i
$146$	−10.3141	+	5.95487i	−0.853604	+	0.492829i
$147$	−1.67846	+	0.427528i	−0.138437	+	0.0352619i
$148$	9.86852	+	9.86852i	0.811187	+	0.811187i
$149$	−5.88131	−	21.9493i	−0.481815	−	1.79816i	−0.593992	−	0.804471i	$-0.702449\pi$
$149$	−5.88131	−	21.9493i	−0.481815	−	1.79816i	0.112177	−	0.993688i	$-0.464218\pi$
$150$	2.27825	−	3.83552i	0.186019	−	0.313169i
$151$	2.19157	−	2.19157i	0.178348	−	0.178348i	−0.612288	−	0.790635i	$-0.709751\pi$
$151$	2.19157	−	2.19157i	0.178348	−	0.178348i	0.790635	+	0.612288i	$0.209751\pi$
$152$	11.7748	+	6.79818i	0.955062	+	0.551406i
$153$	−4.10728	+	2.23754i	−0.332054	+	0.180895i
$154$	3.29605	+	0.883175i	0.265604	+	0.0711683i
$155$	16.3100			1.31005
$156$	−7.40274	+	3.77461i	−0.592694	+	0.302211i
$157$	−4.45258			−0.355354			−0.177677	−	0.984089i	$-0.556858\pi$
$157$	−4.45258			−0.355354			−0.177677	+	0.984089i	$0.556858\pi$
$158$	0.950516	+	0.254690i	0.0756190	+	0.0202621i
$159$	1.68737	−	5.99906i	0.133817	−	0.475757i
$160$	14.3457	+	8.28251i	1.13413	+	0.654790i
$161$	4.36212	−	4.36212i	0.343783	−	0.343783i
$162$	1.55119	+	7.19833i	0.121873	+	0.565555i
$163$	−2.74610	−	10.2486i	−0.215091	−	0.802730i	−0.986135	−	0.165948i	$-0.946932\pi$
$163$	−2.74610	−	10.2486i	−0.215091	−	0.802730i	0.771044	−	0.636782i	$-0.219735\pi$
$164$	−2.93911	−	2.93911i	−0.229506	−	0.229506i
$165$	5.08974	+	19.9821i	0.396236	+	1.55560i
$166$	−3.18963	+	1.84153i	−0.247563	+	0.142931i
$167$	2.27164	−	8.47789i	0.175785	−	0.656039i	−0.820631	−	0.571458i	$-0.806378\pi$
$167$	2.27164	−	8.47789i	0.175785	−	0.656039i	0.996417	−	0.0845812i	$-0.0269553\pi$
$168$	−3.37852	+	3.29584i	−0.260659	+	0.254279i
$169$	−10.7076	−	7.37205i	−0.823662	−	0.567081i
$170$			3.64115i			0.279263i
$171$	−14.3580	−	4.23112i	−1.09798	−	0.323562i
$172$	5.92226	+	10.2576i	0.451568	+	0.782138i
$173$	−6.34253	+	10.9856i	−0.482214	+	0.835219i	−0.999792	−	0.0204176i	$-0.993500\pi$
$173$	−6.34253	+	10.9856i	−0.482214	+	0.835219i	0.517578	+	0.855636i	$0.326834\pi$
$174$	0.284907	+	0.00352961i	0.0215987	+	0.000267579i
$175$	−3.04076	+	0.814769i	−0.229860	+	0.0615907i
$176$	−1.73892	+	0.465942i	−0.131076	+	0.0351217i
$177$	2.36676	+	0.0293210i	0.177897	+	0.00220390i
$178$	5.90465	−	10.2272i	0.442572	−	0.766558i
$179$	1.15864	+	2.00683i	0.0866011	+	0.149997i	0.906072	−	0.423123i	$-0.139066\pi$
$179$	1.15864	+	2.00683i	0.0866011	+	0.149997i	−0.819471	+	0.573120i	$0.805733\pi$
$180$	−10.9297	−	3.22085i	−0.814653	−	0.240068i
$181$			17.6771i			1.31393i	0.753920	+	0.656966i	$0.228160\pi$
$181$			17.6771i			1.31393i	−0.753920	+	0.656966i	$0.771840\pi$
$182$	−2.81692	−	0.875942i	−0.208804	−	0.0649292i
$183$	15.0916	−	14.7223i	1.11561	−	1.08830i
$184$	4.35087	−	16.2377i	0.320750	−	1.19706i
$185$	−25.9286	+	14.9699i	−1.90631	+	1.10061i
$186$	1.99866	+	7.84663i	0.146549	+	0.575343i
$187$	−4.59786	−	4.59786i	−0.336229	−	0.336229i
$188$	1.03939	+	3.87907i	0.0758055	+	0.282910i
$189$	2.76348	−	4.40036i	0.201014	−	0.320079i
$190$	−8.23973	+	8.23973i	−0.597773	+	0.597773i
$191$	−2.87422	−	1.65943i	−0.207971	−	0.120072i	0.392397	−	0.919796i	$-0.371646\pi$
$191$	−2.87422	−	1.65943i	−0.207971	−	0.120072i	−0.600368	+	0.799724i	$0.704979\pi$
$192$	−1.82185	+	6.47718i	−0.131480	+	0.467450i
$193$	0.222690	+	0.0596696i	0.0160296	+	0.00429511i	0.266825	−	0.963745i	$-0.414025\pi$
$193$	0.222690	+	0.0596696i	0.0160296	+	0.00429511i	−0.250795	+	0.968040i	$0.580692\pi$
$194$	−1.52341			−0.109374
$195$	−3.71137	−	17.4356i	−0.265777	−	1.24859i
$196$	1.33059			0.0950421
$197$	−9.80081	−	2.62612i	−0.698279	−	0.187103i	−0.107819	−	0.994170i	$-0.534387\pi$
$197$	−9.80081	−	2.62612i	−0.698279	−	0.187103i	−0.590460	+	0.807067i	$0.701054\pi$
$198$	−8.98956	+	4.89729i	−0.638860	+	0.348035i
$199$	14.4526	+	8.34420i	1.02452	+	0.591505i	0.915409	−	0.402525i	$-0.131868\pi$
$199$	14.4526	+	8.34420i	1.02452	+	0.591505i	0.109107	+	0.994030i	$0.465201\pi$
$200$	−6.06583	+	6.06583i	−0.428919	+	0.428919i
$201$	4.50984	−	7.59248i	0.318099	−	0.535532i
$202$	3.94100	+	14.7080i	0.277288	+	1.03485i
$203$	−0.142172	−	0.142172i	−0.00997852	−	0.00997852i
$204$	3.48194	−	0.886901i	0.243784	−	0.0620955i
$205$	7.72224	−	4.45843i	0.539344	−	0.311391i
$206$	0.0242033	−	0.0903281i	0.00168633	−	0.00629346i
$207$	−0.458481	+	18.5012i	−0.0318666	+	1.28592i
$208$	1.51810	−	0.342858i	0.105261	−	0.0237729i
$209$		−	20.8094i		−	1.43942i
$210$	−1.97902	−	3.52797i	−0.136565	−	0.243453i
$211$	9.48100	+	16.4216i	0.652699	+	1.13051i	0.982465	+	0.186445i	$0.0596965\pi$
$211$	9.48100	+	16.4216i	0.652699	+	1.13051i	−0.329767	+	0.944062i	$0.606970\pi$
$212$	−2.39371	+	4.14602i	−0.164400	+	0.284750i
$213$	0.0663173	−	5.35306i	0.00454399	−	0.366786i
$214$	−6.64786	+	1.78129i	−0.454438	+	0.121766i
$215$	−24.5439	+	6.57651i	−1.67388	+	0.448514i
$216$	0.526105	−	14.1498i	0.0357969	−	0.962769i
$217$	2.85691	−	4.94832i	0.193940	−	0.335914i
$218$	−4.35661	−	7.54588i	−0.295067	−	0.511071i
$219$	−21.9892	+	12.3348i	−1.48589	+	0.833511i
$220$		−	15.8407i		−	1.06798i
$221$	3.81406	+	4.12942i	0.256562	+	0.277775i
$222$	−10.3793	−	10.6397i	−0.696611	−	0.714088i
$223$	2.98727	−	11.1486i	0.200042	−	0.746567i	−0.790862	−	0.611995i	$-0.790367\pi$
$223$	2.98727	−	11.1486i	0.200042	−	0.746567i	0.990904	−	0.134572i	$-0.0429661\pi$
$224$	5.02570	−	2.90159i	0.335793	−	0.193870i
$225$	4.92321	−	8.05932i	0.328214	−	0.537288i
$226$	3.64488	+	3.64488i	0.242454	+	0.242454i
$227$	−4.59122	−	17.1347i	−0.304730	−	1.13727i	−0.933178	−	0.359415i	$-0.882976\pi$
$227$	−4.59122	−	17.1347i	−0.304730	−	1.13727i	0.628448	−	0.777852i	$-0.283690\pi$
$228$	9.88645	+	5.87243i	0.654746	+	0.388911i
$229$	2.52373	−	2.52373i	0.166773	−	0.166773i	−0.618786	−	0.785559i	$-0.712375\pi$
$229$	2.52373	−	2.52373i	0.166773	−	0.166773i	0.785559	+	0.618786i	$0.212375\pi$
$230$	12.4771	+	7.20368i	0.822719	+	0.474997i
$231$	6.95395	+	1.95595i	0.457536	+	0.128692i
$232$	−0.529225	−	0.141805i	−0.0347453	−	0.00930998i
$233$	−6.78563			−0.444541			−0.222271	−	0.974985i	$-0.571347\pi$
$233$	−6.78563			−0.444541			−0.222271	+	0.974985i	$0.571347\pi$
$234$	7.93335	−	3.92211i	0.518619	−	0.256396i
$235$	−8.61520			−0.561994
$236$	−1.75637	−	0.470618i	−0.114330	−	0.0306346i
$237$	2.00538	+	0.564056i	0.130263	+	0.0366394i
$238$	1.10470	+	0.637797i	0.0716068	+	0.0413422i
$239$	−19.5702	+	19.5702i	−1.26589	+	1.26589i	−0.317700	+	0.948191i	$0.602910\pi$
$239$	−19.5702	+	19.5702i	−1.26589	+	1.26589i	−0.948191	+	0.317700i	$0.897090\pi$
$240$	1.83484	+	1.08987i	0.118438	+	0.0703509i
$241$	0.620361	+	2.31522i	0.0399610	+	0.149136i	0.983024	−	0.183478i	$-0.0587358\pi$
$241$	0.620361	+	2.31522i	0.0399610	+	0.149136i	−0.943063	+	0.332615i	$0.892069\pi$
$242$	−3.69938	−	3.69938i	−0.237805	−	0.237805i
$243$	3.09480	+	15.2782i	0.198531	+	0.980095i
$244$	−14.0266	+	8.09825i	−0.897960	+	0.518437i
$245$	−0.738792	+	2.75721i	−0.0471997	+	0.176152i
$246$	3.09123	+	3.16878i	0.197089	+	0.202034i
$247$	−0.713637	+	17.9757i	−0.0454076	+	1.14377i
$248$		−	15.5702i		−	0.988709i
$249$	−6.80012	+	3.81452i	−0.430940	+	0.241736i
$250$	2.16261	+	3.74574i	0.136775	+	0.236902i
$251$	3.41350	−	5.91236i	0.215458	−	0.373185i	−0.737956	−	0.674849i	$-0.764209\pi$
$251$	3.41350	−	5.91236i	0.215458	−	0.373185i	0.953414	+	0.301664i	$0.0975422\pi$
$252$	−2.89167	+	2.75182i	−0.182158	+	0.173348i
$253$	−24.8520	+	6.65906i	−1.56243	+	0.418652i
$254$	10.8256	−	2.90070i	0.679257	−	0.182006i
$255$	−0.0954870	+	7.70761i	−0.00597962	+	0.482669i
$256$	7.33249	−	12.7002i	0.458281	−	0.793765i
$257$	−13.3030	−	23.0414i	−0.829817	−	1.43729i	−0.898181	−	0.439625i	$-0.855111\pi$
$257$	−13.3030	−	23.0414i	−0.829817	−	1.43729i	0.0683638	−	0.997660i	$-0.478222\pi$
$258$	−6.17157	−	11.0020i	−0.384225	−	0.684956i
$259$			10.4887i			0.651737i
$260$	−0.543240	+	13.6836i	−0.0336903	+	0.848620i
$261$	0.603000	+	0.0149430i	0.0373247	+	0.000924949i
$262$	−2.33609	+	8.71840i	−0.144324	+	0.538625i
$263$	5.76930	−	3.33090i	0.355750	−	0.205392i	−0.311465	−	0.950258i	$-0.600820\pi$
$263$	5.76930	−	3.33090i	0.355750	−	0.205392i	0.667215	+	0.744865i	$0.267486\pi$
$264$	19.0758	−	4.85888i	1.17403	−	0.299044i
$265$	−7.26219	−	7.26219i	−0.446113	−	0.446113i
$266$	1.05657	+	3.94317i	0.0647824	+	0.241771i
$267$	12.7672	−	21.4941i	0.781340	−	1.31542i
$268$	−4.79703	+	4.79703i	−0.293025	+	0.293025i
$269$	−4.42577	−	2.55522i	−0.269844	−	0.155794i	0.358973	−	0.933348i	$-0.383127\pi$
$269$	−4.42577	−	2.55522i	−0.269844	−	0.155794i	−0.628817	+	0.777554i	$0.716460\pi$
$270$	11.5971	+	3.57424i	0.705777	+	0.217521i
$271$	−2.88509	−	0.773059i	−0.175257	−	0.0469600i	0.170123	−	0.985423i	$-0.445583\pi$
$271$	−2.88509	−	0.773059i	−0.175257	−	0.0469600i	−0.345380	+	0.938463i	$0.612250\pi$
$272$	−0.672973			−0.0408050
$273$	−5.93991	−	1.92807i	−0.359500	−	0.116692i
$274$	17.7784			1.07403
$275$	12.6820	+	3.39812i	0.764751	+	0.204914i
$276$	3.84955	−	13.6862i	0.231715	−	0.823814i
$277$	−25.9552	−	14.9853i	−1.55950	−	0.900378i	−0.997305	−	0.0733728i	$-0.976624\pi$
$277$	−25.9552	−	14.9853i	−1.55950	−	0.900378i	−0.562195	−	0.827005i	$-0.690043\pi$
$278$	5.12556	−	5.12556i	0.307411	−	0.307411i
$279$	4.02499	+	16.6622i	0.240970	+	0.997541i
$280$	2.01321	+	7.51341i	0.120312	+	0.449012i
$281$	−7.06580	−	7.06580i	−0.421510	−	0.421510i	0.464213	−	0.885724i	$-0.346337\pi$
$281$	−7.06580	−	7.06580i	−0.421510	−	0.421510i	−0.885724	+	0.464213i	$0.846337\pi$
$282$	−1.05572	−	4.14473i	−0.0628674	−	0.246815i
$283$	−13.4820	+	7.78381i	−0.801419	+	0.462700i	−0.843967	−	0.536395i	$-0.819786\pi$
$283$	−13.4820	+	7.78381i	−0.801419	+	0.462700i	0.0425480	+	0.999094i	$0.486452\pi$
$284$	−1.06443	+	3.97249i	−0.0631621	+	0.235724i
$285$	−17.6580	+	17.2258i	−1.04597	+	1.02037i
$286$	8.34780	+	9.03802i	0.493616	+	0.534429i
$287$		−	3.12382i		−	0.184393i
$288$	−4.92113	+	16.6995i	−0.289981	+	0.984029i
$289$	7.28465	+	12.6174i	0.428509	+	0.742199i
$290$	0.234786	−	0.406660i	0.0137871	−	0.0238799i
$291$	−3.22475	−	0.0399504i	−0.189038	−	0.00234193i
$292$	18.7087	−	5.01299i	1.09485	−	0.293363i
$293$	10.0403	−	2.69030i	0.586563	−	0.157169i	0.0466810	−	0.998910i	$-0.485136\pi$
$293$	10.0403	−	2.69030i	0.586563	−	0.157169i	0.539882	+	0.841741i	$0.318469\pi$
$294$	−1.41701	−	0.0175549i	−0.0826418	−	0.00102382i
$295$	1.95040	−	3.37819i	0.113557	−	0.196686i
$296$	14.2909	+	24.7526i	0.830642	+	1.43871i
$297$	−19.1576	+	10.1309i	−1.11164	+	0.587853i
$298$		−	18.5919i		−	1.07700i
$299$	21.6961	−	4.89999i	1.25472	−	0.283374i
$300$	−5.19328	+	5.06618i	−0.299834	+	0.292496i
$301$	−2.30393	+	8.59838i	−0.132796	+	0.495602i
$302$	2.19608	−	1.26791i	0.126370	−	0.0729597i
$303$	7.95663	+	31.2374i	0.457096	+	1.79454i
$304$	−1.52290	−	1.52290i	−0.0873445	−	0.0873445i
$305$	−8.99289	−	33.5619i	−0.514931	−	1.92175i
$306$	−3.71979	+	0.898567i	−0.212646	+	0.0513677i
$307$	0.777977	−	0.777977i	0.0444015	−	0.0444015i	−0.684557	−	0.728959i	$-0.740005\pi$
$307$	0.777977	−	0.777977i	0.0444015	−	0.0444015i	0.728959	+	0.684557i	$0.240005\pi$
$308$	−4.80595	−	2.77472i	−0.273844	−	0.158104i
$309$	0.0536026	−	0.190572i	0.00304934	−	0.0108413i
$310$	12.8897	+	3.45379i	0.732086	+	0.196162i
$311$	−14.8809			−0.843818			−0.421909	−	0.906638i	$-0.638640\pi$
$311$	−14.8809			−0.843818			−0.421909	+	0.906638i	$0.638640\pi$
$312$	−16.6447	+	3.54304i	−0.942323	+	0.200585i
$313$	−10.3784			−0.586624			−0.293312	−	0.956017i	$-0.594758\pi$
$313$	−10.3784			−0.586624			−0.293312	+	0.956017i	$0.594758\pi$
$314$	−3.51885	−	0.942874i	−0.198580	−	0.0532095i
$315$	−4.09667	−	7.51994i	−0.230821	−	0.423701i
$316$	−1.38594	−	0.800173i	−0.0779652	−	0.0450132i
$317$	−13.3620	+	13.3620i	−0.750484	+	0.750484i	−0.974570	−	0.224085i	$-0.928061\pi$
$317$	−13.3620	+	13.3620i	−0.750484	+	0.750484i	0.224085	+	0.974570i	$0.428061\pi$
$318$	2.60388	−	4.38372i	0.146018	−	0.245827i
$319$	0.217035	+	0.809985i	0.0121516	+	0.0453505i
$320$	7.84097	+	7.84097i	0.438324	+	0.438324i
$321$	−14.1189	+	3.59631i	−0.788042	+	0.200726i
$322$	4.37108	−	2.52365i	0.243591	−	0.140637i
$323$	2.01334	−	7.51390i	0.112025	−	0.418085i
$324$	0.593159	−	11.9606i	0.0329533	−	0.664478i
$325$	−10.8384	−	3.37029i	−0.601209	−	0.186950i
$326$		−	8.68092i		−	0.480792i
$327$	−9.02423	−	16.0874i	−0.499041	−	0.889636i
$328$	−4.25621	−	7.37198i	−0.235010	−	0.407050i
$329$	−1.50907	+	2.61379i	−0.0831977	+	0.144103i
$330$	−0.208991	+	16.8696i	−0.0115046	+	0.928639i
$331$	18.8752	−	5.05759i	1.03747	−	0.277990i	0.300408	−	0.953811i	$-0.402877\pi$
$331$	18.8752	−	5.05759i	1.03747	−	0.277990i	0.737066	+	0.675820i	$0.236210\pi$
$332$	5.78564	−	1.55026i	0.317528	−	0.0850815i
$333$	−21.6919	−	22.7943i	−1.18871	−	1.24912i
$334$	3.59054	−	6.21900i	0.196466	−	0.340289i
$335$	−7.27678	−	12.6038i	−0.397573	−	0.688617i
$336$	0.652056	−	0.365770i	0.0355726	−	0.0199544i
$337$		−	28.6066i		−	1.55830i	−0.626836	−	0.779151i	$-0.715650\pi$
$337$		−	28.6066i		−	1.55830i	0.626836	−	0.779151i	$-0.284350\pi$
$338$	−6.90108	−	8.09354i	−0.375369	−	0.440230i
$339$	7.61992	+	7.81109i	0.413857	+	0.424240i
$340$	1.53261	−	5.71980i	0.0831177	−	0.310199i
$341$	−20.6377	+	11.9152i	−1.11760	+	0.645244i
$342$	−10.4511	−	6.38428i	−0.565131	−	0.345222i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	6.27822	+	23.4306i	0.338499	+	1.26329i
$345$	26.2228	+	15.5760i	1.41179	+	0.838584i
$346$	−7.33878	+	7.33878i	−0.394535	+	0.394535i
$347$	12.3139	+	7.10943i	0.661045	+	0.381654i	0.792675	−	0.609645i	$-0.208688\pi$
$347$	12.3139	+	7.10943i	0.661045	+	0.381654i	−0.131630	+	0.991299i	$0.542021\pi$
$348$	−0.446067	−	0.125466i	−0.0239117	−	0.00672568i
$349$	−13.0412	−	3.49437i	−0.698078	−	0.187050i	−0.107709	−	0.994183i	$-0.534351\pi$
$349$	−13.0412	−	3.49437i	−0.698078	−	0.187050i	−0.590370	+	0.807133i	$0.701018\pi$
$350$	−2.57563			−0.137673
$351$	16.8962	−	8.09430i	0.901854	−	0.432042i
$352$	−24.2030			−1.29003
$353$	23.2400	+	6.22714i	1.23694	+	0.331437i	0.817278	−	0.576243i	$-0.195482\pi$
$353$	23.2400	+	6.22714i	1.23694	+	0.331437i	0.419662	+	0.907680i	$0.362149\pi$
$354$	1.86424	+	0.524356i	0.0990830	+	0.0278692i
$355$	−7.64068	−	4.41135i	−0.405525	−	0.234130i
$356$	−13.5802	+	13.5802i	−0.719751	+	0.719751i
$357$	2.32170	+	1.37906i	0.122878	+	0.0729877i
$358$	0.490707	+	1.83134i	0.0259347	+	0.0967895i
$359$	11.4236	+	11.4236i	0.602915	+	0.602915i	0.941085	−	0.338170i	$-0.109808\pi$
$359$	11.4236	+	11.4236i	0.602915	+	0.602915i	−0.338170	+	0.941085i	$0.609808\pi$
$360$	−19.9138	−	12.1648i	−1.04955	−	0.641139i
$361$	5.10518	−	2.94748i	0.268694	−	0.155130i
$362$	−3.74330	+	13.9702i	−0.196743	+	0.734256i
$363$	−7.73386	−	7.92789i	−0.405922	−	0.416106i
$364$	4.05634	+	2.56168i	0.212610	+	0.134269i
$365$			41.5511i			2.17488i
$366$	15.0444	−	8.43917i	0.786386	−	0.441123i
$367$	5.18089	+	8.97357i	0.270440	+	0.468417i	0.968975	−	0.247160i	$-0.0794973\pi$
$367$	5.18089	+	8.97357i	0.270440	+	0.468417i	−0.698534	+	0.715577i	$0.746164\pi$
$368$	−1.33142	+	2.30608i	−0.0694049	+	0.120213i
$369$	6.46043	+	6.78876i	0.336316	+	0.353409i
$370$	−23.6613	+	6.34003i	−1.23009	+	0.329602i
$371$	−3.47536	+	0.931221i	−0.180432	+	0.0483466i
$372$	0.163126	−	13.1674i	0.00845768	−	0.682696i
$373$	14.0992	−	24.4204i	0.730026	−	1.26444i	−0.226845	−	0.973931i	$-0.572841\pi$
$373$	14.0992	−	24.4204i	0.730026	−	1.26444i	0.956871	−	0.290512i	$-0.0938256\pi$
$374$	−2.66003	−	4.60731i	−0.137547	−	0.238238i
$375$	4.47959	+	7.98573i	0.231325	+	0.412381i
$376$			8.22444i			0.424143i
$377$	−0.159702	−	0.707128i	−0.00822509	−	0.0364189i
$378$	3.11579	−	2.89239i	0.160259	−	0.148769i
$379$	−5.98235	+	22.3264i	−0.307293	+	1.14683i	0.623661	+	0.781695i	$0.285645\pi$
$379$	−5.98235	+	22.3264i	−0.307293	+	1.14683i	−0.930954	+	0.365137i	$0.881022\pi$
$380$	16.4118	−	9.47537i	0.841909	−	0.486076i
$381$	22.9917	−	5.85633i	1.17790	−	0.300029i
$382$	−1.92008	−	1.92008i	−0.0982400	−	0.0982400i
$383$	6.67134	+	24.8978i	0.340890	+	1.27222i	0.897341	+	0.441338i	$0.145496\pi$
$383$	6.67134	+	24.8978i	0.340890	+	1.27222i	−0.556451	+	0.830880i	$0.687837\pi$
$384$	7.45489	−	12.5506i	0.380431	−	0.640469i
$385$	8.41813	−	8.41813i	0.429028	−	0.429028i
$386$	0.163355	+	0.0943133i	0.00831458	+	0.00480042i
$387$	−12.7755	−	23.4510i	−0.649416	−	1.19208i
$388$	2.39308	+	0.641224i	0.121490	+	0.0325532i
$389$	15.1943			0.770381			0.385191	−	0.922837i	$-0.374136\pi$
$389$	15.1943			0.770381			0.385191	+	0.922837i	$0.374136\pi$
$390$	0.759055	−	14.5652i	0.0384363	−	0.737536i
$391$	−9.61786			−0.486396
$392$	2.63215	+	0.705283i	0.132944	+	0.0356222i
$393$	−5.17368	+	18.3939i	−0.260978	+	0.927850i
$394$	−7.18944	−	4.15083i	−0.362199	−	0.209116i
$395$	2.42762	−	2.42762i	0.122147	−	0.122147i
$396$	16.1828	−	3.90919i	0.813218	−	0.196444i
$397$	8.66910	+	32.3535i	0.435090	+	1.62378i	0.740852	+	0.671668i	$0.234422\pi$
$397$	8.66910	+	32.3535i	0.435090	+	1.62378i	−0.305762	+	0.952108i	$0.598911\pi$
$398$	9.65485	+	9.65485i	0.483954	+	0.483954i
$399$	2.13315	+	8.37464i	0.106791	+	0.419256i
$400$	1.17679	−	0.679422i	0.0588397	−	0.0339711i
$401$	3.38440	−	12.6307i	0.169009	−	0.630750i	−0.828486	−	0.560010i	$-0.810797\pi$
$401$	3.38440	−	12.6307i	0.169009	−	0.630750i	0.997495	−	0.0707397i	$-0.0225360\pi$
$402$	5.17188	−	5.04531i	0.257950	−	0.251637i
$403$	18.2360	−	9.58489i	0.908399	−	0.477457i
$404$		−	24.7633i		−	1.23202i
$405$	24.4551	+	7.87010i	1.21518	+	0.391068i
$406$	−0.0822518	−	0.142464i	−0.00408209	−	0.00707038i
$407$	21.8724	−	37.8842i	1.08418	−	1.87785i
$408$	7.35802	+	0.0911560i	0.364276	+	0.00451289i
$409$	2.20498	−	0.590822i	0.109029	−	0.0292143i	−0.203892	−	0.978993i	$-0.565359\pi$
$409$	2.20498	−	0.590822i	0.109029	−	0.0292143i	0.312921	+	0.949779i	$0.398692\pi$
$410$	7.04697	−	1.88823i	0.348025	−	0.0932530i
$411$	37.6334	+	0.466227i	1.85632	+	0.0229973i
$412$	−0.0760409	+	0.131707i	−0.00374627	+	0.00648872i
$413$	−0.683278	−	1.18347i	−0.0336219	−	0.0582349i
$414$	−4.28014	+	14.5244i	−0.210357	+	0.713833i
$415$			12.8496i			0.630762i
$416$	20.9072	+	0.830017i	1.02506	+	0.0406949i
$417$	10.9842	−	10.7154i	0.537900	−	0.524736i
$418$	4.40659	−	16.4456i	0.215533	−	0.804381i
$419$	21.3139	−	12.3056i	1.04125	−	0.601168i	0.121066	−	0.992644i	$-0.461369\pi$
$419$	21.3139	−	12.3056i	1.04125	−	0.601168i	0.920188	+	0.391476i	$0.128035\pi$
$420$	1.62381	+	6.37501i	0.0792338	+	0.311069i
$421$	−2.73326	−	2.73326i	−0.133211	−	0.133211i	0.637358	−	0.770568i	$-0.280027\pi$
$421$	−2.73326	−	2.73326i	−0.133211	−	0.133211i	−0.770568	+	0.637358i	$0.780027\pi$
$422$	4.01538	+	14.9856i	0.195465	+	0.729487i
$423$	−2.12607	−	8.80127i	−0.103373	−	0.427932i
$424$	−6.93280	+	6.93280i	−0.336687	+	0.336687i
$425$	4.25045	+	2.45400i	0.206177	+	0.119036i
$426$	1.18597	−	4.21646i	0.0574605	−	0.204288i
$427$	−11.7577	−	3.15045i	−0.568993	−	0.152461i
$428$	11.1927			0.541021
$429$	17.4337	+	19.3507i	0.841705	+	0.934258i
$430$	−20.7896			−1.00256
$431$	−31.6313	−	8.47559i	−1.52363	−	0.408255i	−0.602694	−	0.797973i	$-0.705906\pi$
$431$	−31.6313	−	8.47559i	−1.52363	−	0.408255i	−0.920934	+	0.389718i	$0.872573\pi$
$432$	−0.660606	+	2.14343i	−0.0317834	+	0.103126i
$433$	−7.75704	−	4.47853i	−0.372780	−	0.215224i	0.301893	−	0.953342i	$-0.402382\pi$
$433$	−7.75704	−	4.47853i	−0.372780	−	0.215224i	−0.674672	+	0.738118i	$0.735715\pi$
$434$	3.30566	−	3.30566i	0.158677	−	0.158677i
$435$	0.507660	−	0.854665i	0.0243404	−	0.0409780i
$436$	3.66753	+	13.6874i	0.175643	+	0.655508i
$437$	−21.7647	−	21.7647i	−1.04115	−	1.04115i
$438$	−19.9900	+	5.09175i	−0.955159	+	0.243293i
$439$	29.7227	−	17.1604i	1.41859	−	0.819022i	0.422413	−	0.906403i	$-0.361183\pi$
$439$	29.7227	−	17.1604i	1.41859	−	0.819022i	0.996175	+	0.0873813i	$0.0278499\pi$
$440$	8.39642	−	31.3359i	0.400284	−	1.49388i
$441$	−2.99908	−	0.0743205i	−0.142813	−	0.00353907i
$442$	2.13980	+	4.07113i	0.101780	+	0.193644i
$443$			29.9386i			1.42243i	0.702976	+	0.711213i	$0.251854\pi$
$443$			29.9386i			1.42243i	−0.702976	+	0.711213i	$0.748146\pi$
$444$	11.8262	+	21.0824i	0.561245	+	1.00053i
$445$	−20.6003	−	35.6808i	−0.976550	−	1.69143i
$446$	4.72165	−	8.17814i	0.223577	−	0.387246i
$447$	0.487561	−	39.3554i	0.0230609	−	1.86145i
$448$	3.75234	−	1.00544i	0.177282	−	0.0475024i
$449$	−16.7204	+	4.48023i	−0.789086	+	0.211435i	−0.630787	−	0.775956i	$-0.717268\pi$
$449$	−16.7204	+	4.48023i	−0.789086	+	0.211435i	−0.158299	+	0.987391i	$0.550601\pi$
$450$	5.59743	−	5.32671i	0.263865	−	0.251104i
$451$	−6.51419	+	11.2829i	−0.306741	+	0.531292i
$452$	−4.19147	−	7.25983i	−0.197150	−	0.341474i
$453$	4.68192	−	2.62632i	0.219976	−	0.123395i
$454$		−	14.5137i		−	0.681161i
$455$	−7.56047	+	6.98309i	−0.354440	+	0.327372i
$456$	16.4445	+	16.8571i	0.770085	+	0.789405i
$457$	5.20695	−	19.4326i	0.243571	−	0.909019i	−0.730525	−	0.682886i	$-0.760725\pi$
$457$	5.20695	−	19.4326i	0.243571	−	0.909019i	0.974096	−	0.226134i	$-0.0726086\pi$
$458$	2.52892	−	1.46007i	0.118169	−	0.0682248i
$459$	−7.89764	+	1.80454i	−0.368630	+	0.0842289i
$460$	−16.5679	−	16.5679i	−0.772483	−	0.772483i
$461$	1.35955	+	5.07389i	0.0633204	+	0.236315i	0.990332	−	0.138718i	$-0.0442981\pi$
$461$	1.35955	+	5.07389i	0.0633204	+	0.236315i	−0.927012	+	0.375033i	$0.877631\pi$
$462$	5.08149	+	3.01834i	0.236412	+	0.140426i
$463$	11.4326	−	11.4326i	0.531317	−	0.531317i	−0.389647	−	0.920964i	$-0.627403\pi$
$463$	11.4326	−	11.4326i	0.531317	−	0.531317i	0.920964	+	0.389647i	$0.127403\pi$
$464$	0.0751608	+	0.0433941i	0.00348925	+	0.00201452i
$465$	27.1944	+	7.64902i	1.26111	+	0.354715i
$466$	−5.36266	−	1.43692i	−0.248420	−	0.0665640i
$467$	21.3665			0.988724			0.494362	−	0.869256i	$-0.335402\pi$
$467$	21.3665			0.988724			0.494362	+	0.869256i	$0.335402\pi$
$468$	−14.1132	+	2.82188i	−0.652382	+	0.130441i
$469$	−5.09851			−0.235427
$470$	−6.80856	−	1.82435i	−0.314055	−	0.0841509i
$471$	−7.42401	−	2.08816i	−0.342080	−	0.0962174i
$472$	−3.22497	−	1.86194i	−0.148441	−	0.0857026i
$473$	26.2520	−	26.2520i	1.20707	−	1.20707i
$474$	1.46540	+	0.870429i	0.0673080	+	0.0399801i
$475$	4.06528	+	15.1718i	0.186528	+	0.696131i
$476$	−1.46688	−	1.46688i	−0.0672345	−	0.0672345i
$477$	5.62686	−	9.21121i	0.257636	−	0.421752i
$478$	−19.6104	+	11.3221i	−0.896960	+	0.517860i
$479$	−6.78680	+	25.3287i	−0.310097	+	1.15730i	0.618371	+	0.785886i	$0.287793\pi$
$479$	−6.78680	+	25.3287i	−0.310097	+	1.15730i	−0.928468	+	0.371412i	$0.878874\pi$
$480$	20.0350	+	20.5377i	0.914470	+	0.937413i
$481$	−20.1931	+	31.9752i	−0.920727	+	1.45794i
$482$			1.96108i			0.0893245i
$483$	9.31892	−	5.22744i	0.424026	−	0.237857i
$484$	4.25414	+	7.36839i	0.193370	+	0.334927i
$485$	−2.65745	+	4.60284i	−0.120669	+	0.209004i
$486$	−0.789484	+	12.7296i	−0.0358117	+	0.577427i
$487$	−23.3974	+	6.26930i	−1.06024	+	0.284089i	−0.746475	−	0.665413i	$-0.768255\pi$
$487$	−23.3974	+	6.26930i	−1.06024	+	0.284089i	−0.313760	+	0.949502i	$0.601589\pi$
$488$	−32.0397	+	8.58500i	−1.45037	+	0.388625i
$489$	0.227652	−	18.3758i	0.0102948	−	0.830984i
$490$	−1.16773	+	2.02257i	−0.0527526	+	0.0913703i
$491$	−0.387576	−	0.671300i	−0.0174910	−	0.0302954i	0.857147	−	0.515071i	$-0.172235\pi$
$491$	−0.387576	−	0.671300i	−0.0174910	−	0.0302954i	−0.874638	+	0.484776i	$0.838901\pi$
$492$	−3.52215	−	6.27890i	−0.158791	−	0.283075i
$493$			0.313470i			0.0141180i
$494$	−4.37050	+	14.0550i	−0.196638	+	0.632364i
$495$	−0.884788	+	35.7041i	−0.0397683	+	1.60478i
$496$	−0.638344	+	2.38233i	−0.0286625	+	0.106970i
$497$	−2.67674	+	1.54542i	−0.120068	+	0.0693213i
$498$	−6.18187	+	1.57462i	−0.277016	+	0.0705602i
$499$	−10.0576	−	10.0576i	−0.450241	−	0.450241i	0.445193	−	0.895434i	$-0.353135\pi$
$499$	−10.0576	−	10.0576i	−0.450241	−	0.450241i	−0.895434	+	0.445193i	$0.853135\pi$
$500$	−1.82055	−	6.79437i	−0.0814173	−	0.303854i
$501$	7.76358	−	13.0703i	0.346851	−	0.583937i
$502$	3.94967	−	3.94967i	0.176282	−	0.176282i
$503$	−3.93474	−	2.27173i	−0.175442	−	0.101291i	0.409708	−	0.912217i	$-0.365631\pi$
$503$	−3.93474	−	2.27173i	−0.175442	−	0.101291i	−0.585149	+	0.810926i	$0.698964\pi$
$504$	−7.17886	+	3.91086i	−0.319772	+	0.174204i
$505$	51.3138	+	13.7495i	2.28343	+	0.611844i
$506$	−21.0505			−0.935810
$507$	−14.3960	−	17.3134i	−0.639349	−	0.768917i
$508$	−18.2266			−0.808674
$509$	3.05407	+	0.818336i	0.135369	+	0.0362721i	0.325867	−	0.945415i	$-0.394344\pi$
$509$	3.05407	+	0.818336i	0.135369	+	0.0362721i	−0.190498	+	0.981688i	$0.561010\pi$
$510$	−1.70762	+	6.07107i	−0.0756147	+	0.268832i
$511$	12.6063	+	7.27824i	0.557669	+	0.321970i
$512$	−3.43473	+	3.43473i	−0.151795	+	0.151795i
$513$	−21.9555	−	13.7884i	−0.969360	−	0.608771i
$514$	−5.63406	−	21.0266i	−0.248508	−	0.927443i
$515$	−0.230698	−	0.230698i	−0.0101658	−	0.0101658i
$516$	5.06386	+	19.8805i	0.222924	+	0.875191i
$517$	10.9012	−	6.29381i	0.479434	−	0.276801i
$518$	−2.22108	+	8.28920i	−0.0975888	+	0.364206i
$519$	−15.7272	+	15.3423i	−0.690349	+	0.673453i
$520$	−8.32766	+	26.7807i	−0.365192	+	1.17441i
$521$			1.64170i			0.0719240i	0.999353	+	0.0359620i	$0.0114495\pi$
$521$			1.64170i			0.0719240i	−0.999353	+	0.0359620i	$0.988550\pi$
$522$	0.473384	+	0.139500i	0.0207195	+	0.00610575i
$523$	−6.96712	−	12.0674i	−0.304651	−	0.527671i	0.672533	−	0.740067i	$-0.265206\pi$
$523$	−6.96712	−	12.0674i	−0.304651	−	0.527671i	−0.977184	+	0.212397i	$0.931873\pi$
$524$	7.33941	−	12.7122i	0.320624	−	0.555337i
$525$	−5.45212	−	0.0675445i	−0.237950	−	0.00294788i
$526$	5.26480	−	1.41070i	0.229556	−	0.0615094i
$527$	−8.60472	+	2.30563i	−0.374828	+	0.100435i
$528$	−3.11791	−	0.0386267i	−0.135690	−	0.00168101i
$529$	−7.52807	+	13.0390i	−0.327308	+	0.566913i
$530$	−4.20144	−	7.27712i	−0.182499	−	0.316098i
$531$	3.93247	+	1.15885i	0.170655	+	0.0502898i
$532$		−	6.63896i		−	0.287835i
$533$	6.01405	−	9.52306i	0.260498	−	0.412489i
$534$	14.6414	−	14.2831i	0.633597	−	0.618090i
$535$	−6.21461	+	23.1933i	−0.268681	+	1.00273i
$536$	−12.0321	+	6.94673i	−0.519707	+	0.300053i
$537$	0.990706	+	3.88947i	0.0427521	+	0.167843i
$538$	−2.95658	−	2.95658i	−0.127467	−	0.127467i
$539$	−1.07945	−	4.02854i	−0.0464950	−	0.173522i
$540$	−16.7132	−	10.4961i	−0.719220	−	0.451679i
$541$	10.4049	−	10.4049i	0.447342	−	0.447342i	−0.447128	−	0.894470i	$-0.647553\pi$
$541$	10.4049	−	10.4049i	0.447342	−	0.447342i	0.894470	+	0.447128i	$0.147553\pi$
$542$	−2.11638	−	1.22189i	−0.0909062	−	0.0524847i
$543$	−8.29020	+	29.4740i	−0.355766	+	1.26485i
$544$	−8.73928	−	2.34168i	−0.374694	−	0.100399i
$545$	−30.3990			−1.30215
$546$	−4.28600	−	2.78158i	−0.183424	−	0.119041i
$547$	−16.5893			−0.709309			−0.354654	−	0.934997i	$-0.615401\pi$
$547$	−16.5893			−0.709309			−0.354654	+	0.934997i	$0.615401\pi$
$548$	−27.9276	−	7.48318i	−1.19301	−	0.319666i
$549$	32.0675	−	17.4696i	1.36861	−	0.745583i
$550$	9.30292	+	5.37104i	0.396678	+	0.229022i
$551$	−0.709365	+	0.709365i	−0.0302200	+	0.0302200i
$552$	14.8695	−	25.0334i	0.632889	−	1.06549i
$553$	−0.311290	−	1.16175i	−0.0132374	−	0.0494027i
$554$	−17.3391	−	17.3391i	−0.736666	−	0.736666i
$555$	−50.2527	+	12.8001i	−2.13311	+	0.543334i
$556$	−10.2090	+	5.89420i	−0.432960	+	0.249970i
$557$	−5.46067	+	20.3795i	−0.231376	+	0.863507i	0.748373	+	0.663278i	$0.230835\pi$
$557$	−5.46067	+	20.3795i	−0.231376	+	0.863507i	−0.979749	+	0.200229i	$0.935831\pi$
$558$	−0.347442	+	14.0204i	−0.0147084	+	0.593532i
$559$	−23.5774	+	21.7768i	−0.997217	+	0.921061i
$560$		−	1.23213i		−	0.0520671i
$561$	−5.50995	−	9.82254i	−0.232630	−	0.414708i
$562$	−4.08783	−	7.08032i	−0.172435	−	0.298665i
$563$	12.3986	−	21.4750i	0.522539	−	0.905064i	−0.477117	−	0.878840i	$-0.658318\pi$
$563$	12.3986	−	21.4750i	0.522539	−	0.905064i	0.999656	−	0.0262243i	$-0.00834842\pi$
$564$	−0.0861658	+	6.95522i	−0.00362824	+	0.292868i
$565$	17.3709	−	4.65451i	0.730798	−	0.195817i
$566$	−12.3030	+	3.29659i	−0.517135	+	0.138566i
$567$	6.67137	−	6.04093i	0.280171	−	0.253695i
$568$	−4.21126	+	7.29412i	−0.176701	+	0.306055i
$569$	17.5972	+	30.4793i	0.737714	+	1.27776i	0.953522	+	0.301322i	$0.0974279\pi$
$569$	17.5972	+	30.4793i	0.737714	+	1.27776i	−0.215809	+	0.976436i	$0.569239\pi$
$570$	−17.6028	+	9.87427i	−0.737299	+	0.413587i
$571$			30.6303i			1.28184i	0.767609	+	0.640918i	$0.221446\pi$
$571$			30.6303i			1.28184i	−0.767609	+	0.640918i	$0.778554\pi$
$572$	−9.30912	−	17.7113i	−0.389234	−	0.740548i
$573$	−4.01409	−	4.11480i	−0.167691	−	0.171898i
$574$	0.661498	−	2.46874i	0.0276104	−	0.103043i
$575$	16.8183	−	9.71003i	0.701370	−	0.404936i
$576$	−6.07531	+	9.94532i	−0.253138	+	0.414388i
$577$	25.5152	+	25.5152i	1.06221	+	1.06221i	0.997932	+	0.0642810i	$0.0204754\pi$
$577$	25.5152	+	25.5152i	1.06221	+	1.06221i	0.0642810	+	0.997932i	$0.479525\pi$
$578$	3.08518	+	11.5141i	0.128327	+	0.478922i
$579$	0.343319	+	0.203927i	0.0142678	+	0.00847492i
$580$	−0.539988	+	0.539988i	−0.0224218	+	0.0224218i
$581$	3.89847	+	2.25078i	0.161736	+	0.0933782i
$582$	−2.54005	−	0.714444i	−0.105289	−	0.0296147i
$583$	14.4945	+	3.88380i	0.600303	+	0.160851i
$584$	39.6665			1.64141
$585$	1.98874	−	30.8117i	0.0822241	−	1.27391i
$586$	8.50454			0.351319
$587$	−10.6918	−	2.86485i	−0.441297	−	0.118245i	0.0313274	−	0.999509i	$-0.490027\pi$
$587$	−10.6918	−	2.86485i	−0.441297	−	0.118245i	−0.472624	+	0.881264i	$0.656693\pi$
$588$	2.21856	+	0.624018i	0.0914919	+	0.0257341i
$589$	−24.6896	−	14.2545i	−1.01732	−	0.587347i
$590$	2.25676	−	2.25676i	0.0929092	−	0.0929092i
$591$	−15.1098	−	8.97503i	−0.621534	−	0.369184i
$592$	−1.17179	−	4.37319i	−0.0481603	−	0.179737i
$593$	27.8346	+	27.8346i	1.14303	+	1.14303i	0.987893	+	0.155135i	$0.0495813\pi$
$593$	27.8346	+	27.8346i	1.14303	+	1.14303i	0.155135	+	0.987893i	$0.450419\pi$
$594$	−17.2855	+	3.94959i	−0.709232	+	0.162054i
$595$	3.85410	−	2.22517i	0.158003	−	0.0912229i
$596$	−7.82561	+	29.2056i	−0.320549	+	1.19631i
$597$	20.1843	+	20.6907i	0.826087	+	0.846812i
$598$	18.1839	+	0.721905i	0.743597	+	0.0295209i
$599$			29.6554i			1.21169i	0.795584	+	0.605843i	$0.207164\pi$
$599$			29.6554i			1.21169i	−0.795584	+	0.605843i	$0.792836\pi$
$600$	−12.9586	+	7.26913i	−0.529033	+	0.296761i
$601$	1.75504	+	3.03982i	0.0715897	+	0.123997i	0.899598	−	0.436719i	$-0.143859\pi$
$601$	1.75504	+	3.03982i	0.0715897	+	0.123997i	−0.828008	+	0.560716i	$0.810526\pi$
$602$	−3.64157	+	6.30739i	−0.148419	+	0.257070i
$603$	11.0802	−	10.5443i	0.451220	−	0.429397i
$604$	−3.98344	+	1.06736i	−0.162084	+	0.0434303i
$605$	−17.6306	+	4.72411i	−0.716787	+	0.192063i
$606$	−0.326710	+	26.3717i	−0.0132717	+	1.07128i
$607$	−5.68065	+	9.83918i	−0.230571	+	0.399360i	−0.957976	−	0.286848i	$-0.907393\pi$
$607$	−5.68065	+	9.83918i	−0.230571	+	0.399360i	0.727406	+	0.686208i	$0.240726\pi$
$608$	−14.4774	−	25.0756i	−0.587137	−	1.01695i
$609$	−0.170375	−	0.303726i	−0.00690394	−	0.0123076i
$610$		−	28.4282i		−	1.15102i
$611$	−9.63256	+	5.06290i	−0.389692	+	0.204823i
$612$	6.22155	+	0.154177i	0.251491	+	0.00623223i
$613$	9.19083	−	34.3006i	0.371214	−	1.38539i	−0.487584	−	0.873076i	$-0.662122\pi$
$613$	9.19083	−	34.3006i	0.371214	−	1.38539i	0.858798	−	0.512314i	$-0.171212\pi$
$614$	0.779576	−	0.450088i	0.0314611	−	0.0181641i
$615$	14.9666	−	3.81221i	0.603511	−	0.153723i
$616$	−8.03631	−	8.03631i	−0.323792	−	0.323792i
$617$	3.87974	+	14.4794i	0.156192	+	0.582918i	0.999000	+	0.0447034i	$0.0142343\pi$
$617$	3.87974	+	14.4794i	0.156192	+	0.582918i	−0.842808	+	0.538214i	$0.819099\pi$
$618$	0.0827174	−	0.139258i	0.00332738	−	0.00560177i
$619$	4.50349	−	4.50349i	0.181011	−	0.181011i	−0.610786	−	0.791796i	$-0.709146\pi$
$619$	4.50349	−	4.50349i	0.181011	−	0.181011i	0.791796	+	0.610786i	$0.209146\pi$
$620$	−18.7944	−	10.8509i	−0.754800	−	0.435784i
$621$	−9.44112	+	30.6330i	−0.378859	+	1.22926i
$622$	−11.7603	−	3.15117i	−0.471545	−	0.126350i
$623$	−14.4337			−0.578275
$624$	2.69200	+	0.140292i	0.107766	+	0.00561617i
$625$	30.8301			1.23320
$626$	−8.20204	−	2.19773i	−0.327820	−	0.0878390i
$627$	9.75917	−	34.6966i	0.389744	−	1.38565i
$628$	5.13081	+	2.96228i	0.204742	+	0.118208i
$629$	11.5631	−	11.5631i	0.461051	−	0.461051i
$630$	−1.64517	−	6.81049i	−0.0655451	−	0.271336i
$631$	−5.18970	−	19.3682i	−0.206599	−	0.771037i	−0.988956	−	0.148207i	$-0.952650\pi$
$631$	−5.18970	−	19.3682i	−0.206599	−	0.771037i	0.782358	−	0.622829i	$-0.214017\pi$
$632$	−2.31751	−	2.31751i	−0.0921857	−	0.0921857i
$633$	8.10679	+	31.8269i	0.322216	+	1.26501i
$634$	−13.3895	+	7.73041i	−0.531763	+	0.307014i
$635$	10.1201	−	37.7686i	0.401603	−	1.49880i
$636$	−5.93554	+	5.79027i	−0.235359	+	0.229599i
$637$	0.794296	+	3.51697i	0.0314712	+	0.139348i
$638$			0.686088i			0.0271625i
$639$	2.62105	−	8.89433i	0.103687	−	0.351854i
$640$	−12.0287	−	20.8344i	−0.475477	−	0.823550i
$641$	0.00284055	−	0.00491998i	0.000112195	−	0.000194327i	−0.865969	−	0.500097i	$-0.833298\pi$
$641$	0.00284055	−	0.00491998i	0.000112195	−	0.000194327i	0.866081	+	0.499903i	$0.166631\pi$
$642$	−11.9197	−	0.147669i	−0.470433	−	0.00582803i
$643$	−21.2274	+	5.68787i	−0.837127	+	0.224308i	−0.651821	−	0.758373i	$-0.725994\pi$
$643$	−21.2274	+	5.68787i	−0.837127	+	0.224308i	−0.185307	+	0.982681i	$0.559328\pi$
$644$	−7.92867	+	2.12448i	−0.312433	+	0.0837163i
$645$	−44.0075	−	0.545194i	−1.73279	−	0.0214670i
$646$	3.18228	−	5.51187i	0.125205	−	0.216861i
$647$	6.66723	+	11.5480i	0.262116	+	0.453998i	0.966804	−	0.255519i	$-0.0822464\pi$
$647$	6.66723	+	11.5480i	0.262116	+	0.453998i	−0.704688	+	0.709517i	$0.748913\pi$
$648$	7.51313	−	23.3459i	0.295144	−	0.917113i
$649$			5.69944i			0.223722i
$650$	−7.85189	−	4.95867i	−0.307977	−	0.194495i
$651$	7.08413	−	6.91075i	0.277649	−	0.270854i
$652$	−3.65393	+	13.6367i	−0.143099	+	0.534052i
$653$	1.75476	−	1.01311i	0.0686691	−	0.0396461i	−0.465272	−	0.885168i	$-0.654044\pi$
$653$	1.75476	−	1.01311i	0.0686691	−	0.0396461i	0.533941	+	0.845521i	$0.320710\pi$
$654$	−3.72515	−	14.6248i	−0.145665	−	0.571874i
$655$	22.2668	+	22.2668i	0.870037	+	0.870037i
$656$	0.348991	+	1.30245i	0.0136258	+	0.0508522i
$657$	−42.4485	+	10.2540i	−1.65607	+	0.400048i
$658$	−1.74611	+	1.74611i	−0.0680703	+	0.0680703i
$659$	−43.3365	−	25.0203i	−1.68815	−	0.974654i	−0.955934	−	0.293582i	$-0.905153\pi$
$659$	−43.3365	−	25.0203i	−1.68815	−	0.974654i	−0.732217	−	0.681072i	$-0.761514\pi$
$660$	7.42895	−	26.4120i	0.289172	−	1.02809i
$661$	41.0599	+	11.0020i	1.59704	+	0.427926i	0.944148	−	0.329522i	$-0.106888\pi$
$661$	41.0599	+	11.0020i	1.59704	+	0.427926i	0.652895	+	0.757448i	$0.273554\pi$
$662$	15.9880			0.621391
$663$	4.42277	+	8.67391i	0.171766	+	0.336867i
$664$	12.2668			0.476044
$665$	13.7571	+	3.68619i	0.533476	+	0.142944i
$666$	−12.3161	−	22.6077i	−0.477240	−	0.876031i
$667$	1.07417	+	0.620171i	0.0415919	+	0.0240131i
$668$	−8.25797	+	8.25797i	−0.319511	+	0.319511i
$669$	10.2093	−	17.1877i	0.394714	−	0.664515i
$670$	−3.08185	−	11.5016i	−0.119062	−	0.444346i
$671$	35.8977	+	35.8977i	1.38581	+	1.38581i
$672$	9.74038	−	2.48102i	0.375743	−	0.0957075i
$673$	−18.1948	+	10.5048i	−0.701358	+	0.404929i	−0.807853	−	0.589384i	$-0.799371\pi$
$673$	−18.1948	+	10.5048i	−0.701358	+	0.404929i	0.106495	+	0.994313i	$0.466037\pi$
$674$	6.05772	−	22.6077i	0.233335	−	0.870816i
$675$	11.9884	−	11.1288i	0.461432	−	0.428349i
$676$	7.43405	+	15.6187i	0.285925	+	0.600720i
$677$		−	29.8206i		−	1.14610i	−0.819521	−	0.573049i	$-0.805761\pi$
$677$		−	29.8206i		−	1.14610i	0.819521	−	0.573049i	$-0.194239\pi$
$678$	4.36792	+	7.78666i	0.167749	+	0.299045i
$679$	0.930978	+	1.61250i	0.0357277	+	0.0618821i
$680$	6.06359	−	10.5024i	0.232528	−	0.402750i
$681$	0.380613	−	30.7227i	0.0145851	−	1.17729i
$682$	−18.8331	+	5.04631i	−0.721156	+	0.193233i
$683$	−26.6875	+	7.15089i	−1.02117	+	0.273621i	−0.730289	−	0.683139i	$-0.760614\pi$
$683$	−26.6875	+	7.15089i	−1.02117	+	0.273621i	−0.290879	+	0.956760i	$0.593948\pi$
$684$	13.7301	+	14.4279i	0.524985	+	0.551666i
$685$	31.0129	−	53.7159i	1.18494	−	2.05238i
$686$	0.409087	+	0.708560i	0.0156190	+	0.0270530i
$687$	5.39153	−	3.02437i	0.205700	−	0.115387i
$688$		−	3.84242i		−	0.146491i
$689$	−12.3875	−	3.85200i	−0.471928	−	0.146749i
$690$	17.4254	+	17.8626i	0.663374	+	0.680017i
$691$	−0.534242	+	1.99382i	−0.0203235	+	0.0758484i	−0.975343	−	0.220695i	$-0.929167\pi$
$691$	−0.534242	+	1.99382i	−0.0203235	+	0.0758484i	0.955019	+	0.296544i	$0.0958340\pi$
$692$	14.6173	−	8.43931i	0.555667	−	0.320814i
$693$	10.6774	+	6.52250i	0.405600	+	0.247769i
$694$	8.22614	+	8.22614i	0.312260	+	0.312260i
$695$	−6.54535	−	24.4276i	−0.248279	−	0.926590i
$696$	−0.815900	−	0.484634i	−0.0309266	−	0.0183700i
$697$	−3.44380	+	3.44380i	−0.130443	+	0.130443i
$698$	−9.56643	−	5.52318i	−0.362095	−	0.209055i
$699$	−11.3140	−	3.18231i	−0.427936	−	0.120366i
$700$	4.04600	+	1.08412i	0.152925	+	0.0409760i
$701$	32.8749			1.24167			0.620835	−	0.783941i	$-0.286794\pi$
$701$	32.8749			1.24167			0.620835	+	0.783941i	$0.286794\pi$
$702$	15.0671	−	2.81896i	0.568670	−	0.106395i
$703$	52.3333			1.97379
$704$	−15.6497	−	4.19333i	−0.589821	−	0.158042i
$705$	−14.3646	−	4.04034i	−0.541001	−	0.152168i
$706$	17.0478	+	9.84257i	0.641603	+	0.370430i
$707$	13.1598	−	13.1598i	0.494925	−	0.494925i
$708$	−2.70777	−	1.60838i	−0.101764	−	0.0604467i
$709$	2.48674	+	9.28063i	0.0933914	+	0.348542i	0.996771	−	0.0803011i	$-0.0255882\pi$
$709$	2.48674	+	9.28063i	0.0933914	+	0.348542i	−0.903379	+	0.428843i	$0.858922\pi$
$710$	−5.10426	−	5.10426i	−0.191559	−	0.191559i
$711$	3.07914	+	1.88096i	0.115477	+	0.0705415i
$712$	−34.0625	+	19.6660i	−1.27654	+	0.737013i
$713$	−9.12296	+	34.0473i	−0.341657	+	1.27508i
$714$	1.54280	+	1.58151i	0.0577380	+	0.0591865i
$715$	41.8697	−	9.45612i	1.56584	−	0.353639i
$716$		−	3.08336i		−	0.115231i
$717$	−41.8084	+	23.4524i	−1.56136	+	0.875846i
$718$	6.60898	+	11.4471i	0.246645	+	0.427202i
$719$	−12.7202	+	22.0320i	−0.474382	+	0.821654i	−0.999570	−	0.0293324i	$-0.990662\pi$
$719$	−12.7202	+	22.0320i	−0.474382	+	0.821654i	0.525187	+	0.850987i	$0.323995\pi$
$720$	2.54820	+	2.67770i	0.0949657	+	0.0997920i
$721$	−0.110402	+	0.0295821i	−0.00411158	+	0.00110170i
$722$	4.65876	−	1.24831i	0.173381	−	0.0464573i
$723$	−0.0514280	+	4.15122i	−0.00191263	+	0.154385i
$724$	11.7605	−	20.3698i	0.437076	−	0.757038i
$725$	−0.316473	−	0.548148i	−0.0117535	−	0.0203577i
$726$	−4.43324	−	7.90309i	−0.164533	−	0.293311i
$727$		−	21.7970i		−	0.808405i	−0.914670	−	0.404202i	$-0.867549\pi$
$727$		−	21.7970i		−	0.808405i	0.914670	−	0.404202i	$-0.132451\pi$
$728$	6.66636	+	7.21755i	0.247072	+	0.267500i
$729$	−2.00501	+	26.9255i	−0.0742597	+	0.997239i
$730$	−8.79883	+	32.8377i	−0.325659	+	1.21538i
$731$	12.0190	−	6.93920i	0.444540	−	0.256655i
$732$	−27.1851	+	6.92446i	−1.00479	+	0.255935i
$733$	−5.40317	−	5.40317i	−0.199570	−	0.199570i	0.600245	−	0.799816i	$-0.295070\pi$
$733$	−5.40317	−	5.40317i	−0.199570	−	0.199570i	−0.799816	+	0.600245i	$0.795070\pi$
$734$	2.19420	+	8.18888i	0.0809895	+	0.302257i
$735$	−2.52490	+	4.25076i	−0.0931323	+	0.156792i
$736$	−25.3141	+	25.3141i	−0.933091	+	0.933091i
$737$	18.4153	+	10.6321i	0.678335	+	0.391637i
$738$	3.66807	+	6.73318i	0.135024	+	0.247852i
$739$	12.5755	+	3.36960i	0.462598	+	0.123953i	0.482588	−	0.875847i	$-0.339697\pi$
$739$	12.5755	+	3.36960i	0.462598	+	0.123953i	−0.0199899	+	0.999800i	$0.506363\pi$
$740$	39.8376			1.46446
$741$	−9.62009	+	29.6371i	−0.353403	+	1.08875i
$742$	−2.94376			−0.108069
$743$	1.89969	+	0.509021i	0.0696930	+	0.0186742i	0.293497	−	0.955960i	$-0.405181\pi$
$743$	1.89969	+	0.509021i	0.0696930	+	0.0186742i	−0.223804	+	0.974634i	$0.571848\pi$
$744$	7.30209	−	25.9610i	0.267708	−	0.951776i
$745$	−56.1739	−	32.4320i	−2.05805	−	1.18822i
$746$	16.3138	−	16.3138i	0.597289	−	0.597289i
$747$	−13.1271	+	3.17104i	−0.480296	+	0.116022i
$748$	2.23929	+	8.35716i	0.0818767	+	0.305568i
$749$	5.94808	+	5.94808i	0.217338	+	0.217338i
$750$	1.84915	+	7.25968i	0.0675214	+	0.265086i
$751$	2.52310	−	1.45671i	0.0920693	−	0.0531562i	−0.453258	−	0.891379i	$-0.649739\pi$
$751$	2.52310	−	1.45671i	0.0920693	−	0.0531562i	0.545328	+	0.838223i	$0.316405\pi$
$752$	0.337184	−	1.25839i	0.0122958	−	0.0458887i
$753$	8.46427	−	8.25711i	0.308455	−	0.300906i
$754$	0.0235286	−	0.592659i	0.000856862	−	0.0215834i
$755$		−	8.84702i		−	0.321976i
$756$	−6.11197	+	3.23211i	−0.222290	+	0.117551i
$757$	16.2355	+	28.1207i	0.590089	+	1.02206i	0.994220	+	0.107363i	$0.0342408\pi$
$757$	16.2355	+	28.1207i	0.590089	+	1.02206i	−0.404131	+	0.914701i	$0.632426\pi$
$758$	−9.45566	+	16.3777i	−0.343445	+	0.594864i
$759$	−44.5599	−	0.552037i	−1.61742	−	0.0200377i
$760$	37.4881	−	10.0449i	1.35983	−	0.364367i
$761$	15.9113	−	4.26343i	0.576786	−	0.154549i	0.0413789	−	0.999144i	$-0.486825\pi$
$761$	15.9113	−	4.26343i	0.576786	−	0.154549i	0.535407	+	0.844594i	$0.320158\pi$
$762$	19.4104	+	0.240469i	0.703164	+	0.00871126i
$763$	−5.32480	+	9.22282i	−0.192771	+	0.333888i
$764$	2.20802	+	3.82440i	0.0798834	+	0.138362i
$765$	−3.77391	+	12.8065i	−0.136446	+	0.463020i
$766$			21.0894i			0.761989i
$767$	0.195456	−	4.92331i	0.00705751	−	0.177770i
$768$	18.1820	−	17.7370i	0.656086	−	0.640028i
$769$	−6.51937	+	24.3306i	−0.235095	+	0.877385i	0.743012	+	0.669279i	$0.233397\pi$
$769$	−6.51937	+	24.3306i	−0.235095	+	0.877385i	−0.978106	+	0.208107i	$0.933270\pi$
$770$	8.43543	−	4.87020i	0.303992	−	0.175510i
$771$	−11.3748	−	44.6570i	−0.409654	−	1.60828i
$772$	−0.216913	−	0.216913i	−0.00780688	−	0.00780688i
$773$	12.1083	+	45.1888i	0.435506	+	1.62533i	0.739854	+	0.672768i	$0.234895\pi$
$773$	12.1083	+	45.1888i	0.435506	+	1.62533i	−0.304348	+	0.952561i	$0.598439\pi$
$774$	−5.13047	−	21.2386i	−0.184411	−	0.763404i
$775$	12.7189	−	12.7189i	0.456877	−	0.456877i
$776$	4.39407	+	2.53692i	0.157738	+	0.0910701i
$777$	−4.91898	+	17.4884i	−0.176468	+	0.627392i
$778$	12.0080	+	3.21753i	0.430507	+	0.115354i
$779$	−15.5863			−0.558436
$780$	−7.32308	+	22.5606i	−0.262208	+	0.807798i
$781$	12.8908			0.461269
$782$	−7.60096	−	2.03667i	−0.271810	−	0.0728312i
$783$	0.998404	+	0.307709i	0.0356800	+	0.0109966i
$784$	−0.373820	−	0.215825i	−0.0133507	−	0.00770803i
$785$	−8.98716	+	8.98716i	−0.320765	+	0.320765i
$786$	−7.98382	+	13.4411i	−0.284773	+	0.479427i
$787$	1.92327	+	7.17775i	0.0685572	+	0.255859i	0.991695	−	0.128609i	$-0.0410514\pi$
$787$	1.92327	+	7.17775i	0.0685572	+	0.255859i	−0.923138	+	0.384469i	$0.874385\pi$
$788$	9.54658	+	9.54658i	0.340083	+	0.340083i
$789$	11.1816	−	2.84811i	0.398074	−	0.101395i
$790$	2.43261	−	1.40447i	0.0865484	−	0.0499687i
$791$	1.63060	−	6.08549i	0.0579775	−	0.216375i
$792$	34.0847	+	0.844657i	1.21115	+	0.0300136i
$793$	−29.7782	−	32.2403i	−1.05746	−	1.14489i
$794$			27.4046i			0.972554i
$795$	−8.70281	−	15.5144i	−0.308657	−	0.550240i
$796$	−11.1027	−	19.2305i	−0.393525	−	0.681605i
$797$	−12.6264	+	21.8695i	−0.447248	+	0.774657i	−0.998206	−	0.0598765i	$-0.980929\pi$
$797$	−12.6264	+	21.8695i	−0.447248	+	0.774657i	0.550958	+	0.834533i	$0.314263\pi$
$798$	−0.0875898	+	7.07016i	−0.00310064	+	0.250281i
$799$	4.54516	−	1.21787i	0.160796	−	0.0430852i
$800$	17.6461	−	4.72825i	0.623882	−	0.167169i
$801$	31.3677	−	29.8506i	1.10832	−	1.05472i
$802$	5.34936	−	9.26536i	0.188892	−	0.327171i
$803$	−30.3550	−	52.5765i	−1.07121	−	1.85538i
$804$	−10.2480	+	5.74863i	−0.361420	+	0.202738i
$805$		−	17.6092i		−	0.620641i
$806$	16.4415	−	3.71326i	0.579128	−	0.130794i
$807$	−6.18097	−	6.33604i	−0.217580	−	0.223039i
$808$	13.1259	−	48.9864i	0.461766	−	1.72333i
$809$	−10.7806	+	6.22418i	−0.379026	+	0.218831i	−0.677394	−	0.735620i	$-0.736891\pi$
$809$	−10.7806	+	6.22418i	−0.379026	+	0.218831i	0.298369	+	0.954451i	$0.403558\pi$
$810$	17.6602	+	11.3983i	0.620516	+	0.400495i
$811$	5.60676	+	5.60676i	0.196880	+	0.196880i	0.798661	−	0.601781i	$-0.205542\pi$
$811$	5.60676	+	5.60676i	0.196880	+	0.196880i	−0.601781	+	0.798661i	$0.705542\pi$
$812$	0.0692420	+	0.258415i	0.00242992	+	0.00906858i
$813$	−4.44792	−	2.64201i	−0.155995	−	0.0926592i
$814$	25.3080	−	25.3080i	0.887045	−	0.887045i
$815$	−26.2287	−	15.1431i	−0.918751	−	0.530441i
$816$	−1.12208	−	0.315610i	−0.0392808	−	0.0110486i
$817$	42.9015	+	11.4954i	1.50093	+	0.402174i
$818$	1.86770			0.0653025
$819$	−8.99969	−	6.00046i	−0.314475	−	0.209673i
$820$	−11.8647			−0.414333
$821$	7.40649	+	1.98456i	0.258488	+	0.0692617i	0.385736	−	0.922609i	$-0.373948\pi$
$821$	7.40649	+	1.98456i	0.258488	+	0.0692617i	−0.127248	+	0.991871i	$0.540614\pi$
$822$	29.6428	+	8.33767i	1.03391	+	0.290810i
$823$	−8.08358	−	4.66706i	−0.281776	−	0.162683i	0.352451	−	0.935830i	$-0.385348\pi$
$823$	−8.08358	−	4.66706i	−0.281776	−	0.162683i	−0.634227	+	0.773147i	$0.718682\pi$
$824$	−0.220234	+	0.220234i	−0.00767223	+	0.00767223i
$825$	19.5516	+	11.6134i	0.680700	+	0.404327i
$826$	−0.289381	−	1.07998i	−0.0100689	−	0.0375775i
$827$	8.19132	+	8.19132i	0.284840	+	0.284840i	0.835036	−	0.550196i	$-0.185447\pi$
$827$	8.19132	+	8.19132i	0.284840	+	0.284840i	−0.550196	+	0.835036i	$0.685447\pi$
$828$	12.8371	−	21.0144i	0.446120	−	0.730300i
$829$	3.98474	−	2.30059i	0.138396	−	0.0799028i	−0.429204	−	0.903208i	$-0.641206\pi$
$829$	3.98474	−	2.30059i	0.138396	−	0.0799028i	0.567599	+	0.823305i	$0.307872\pi$
$830$	−2.72102	+	10.1550i	−0.0944480	+	0.352485i
$831$	−36.2487	−	37.1582i	−1.25745	−	1.28900i
$832$	13.3748	+	4.15899i	0.463688	+	0.144187i
$833$		−	1.55907i		−	0.0540187i
$834$	10.9499	−	6.14233i	0.379163	−	0.212692i
$835$	−12.5268	−	21.6971i	−0.433508	−	0.750858i
$836$	−13.8444	+	23.9792i	−0.478819	+	0.829338i
$837$	−1.10314	+	29.6694i	−0.0381302	+	1.02552i
$838$	19.4502	−	5.21165i	0.671894	−	0.180034i
$839$	15.0803	−	4.04076i	0.520630	−	0.139502i	0.0110722	−	0.999939i	$-0.496476\pi$
$839$	15.0803	−	4.04076i	0.520630	−	0.139502i	0.509558	+	0.860436i	$0.329809\pi$
$840$	−0.166896	+	13.4716i	−0.00575845	+	0.464816i
$841$	−14.4798	+	25.0797i	−0.499303	+	0.864818i
$842$	−1.58129	−	2.73887i	−0.0544948	−	0.0943878i
$843$	−8.46746	−	15.0949i	−0.291635	−	0.519895i
$844$		−	25.2306i		−	0.868474i
$845$	−36.4923	+	6.73255i	−1.25537	+	0.231607i
$846$	0.183525	−	7.40582i	0.00630971	−	0.254617i
$847$	−1.65499	+	6.17649i	−0.0568660	+	0.212227i
$848$	1.34499	−	0.776530i	0.0461871	−	0.0266661i
$849$	−26.1296	+	6.65560i	−0.896765	+	0.228420i
$850$	2.83946	+	2.83946i	0.0973926	+	0.0973926i
$851$	−16.7468	−	62.4998i	−0.574072	−	2.14247i
$852$	−3.63779	+	6.12435i	−0.124628	+	0.209817i
$853$	30.5255	−	30.5255i	1.04517	−	1.04517i	0.0462437	−	0.998930i	$-0.485275\pi$
$853$	30.5255	−	30.5255i	1.04517	−	1.04517i	0.998930	−	0.0462437i	$-0.0147251\pi$
$854$	−8.62489	−	4.97958i	−0.295138	−	0.170398i
$855$	−37.5206	+	20.4403i	−1.28318	+	0.699043i
$856$	22.1413	+	5.93274i	0.756773	+	0.202777i
$857$	−24.3753			−0.832645			−0.416323	−	0.909217i	$-0.636681\pi$
$857$	−24.3753			−0.832645			−0.416323	+	0.909217i	$0.636681\pi$
$858$	9.68008	+	18.9845i	0.330472	+	0.648120i
$859$	−31.4233			−1.07215			−0.536074	−	0.844171i	$-0.680093\pi$
$859$	−31.4233			−1.07215			−0.536074	+	0.844171i	$0.680093\pi$
$860$	32.6578	+	8.75064i	1.11362	+	0.298394i
$861$	1.46500	−	5.20851i	0.0499272	−	0.177505i
$862$	−23.2033	−	13.3965i	−0.790309	−	0.456285i
$863$	−0.505034	+	0.505034i	−0.0171916	+	0.0171916i	−0.715650	−	0.698459i	$-0.753870\pi$
$863$	−0.505034	+	0.505034i	−0.0171916	+	0.0171916i	0.698459	+	0.715650i	$0.253870\pi$
$864$	−16.0370	+	25.5361i	−0.545589	+	0.868754i
$865$	9.37163	+	34.9754i	0.318645	+	1.18920i
$866$	−5.18199	−	5.18199i	−0.176091	−	0.176091i
$867$	6.22879	+	24.4539i	0.211541	+	0.830499i
$868$	−6.58418	+	3.80138i	−0.223482	+	0.129027i
$869$	−1.29829	+	4.84527i	−0.0440413	+	0.164364i
$870$	0.582185	−	0.567936i	0.0197379	−	0.0192548i
$871$	−15.5429	−	9.81576i	−0.526652	−	0.332594i
$872$			29.0202i			0.982748i
$873$	−5.35806	−	1.57895i	−0.181343	−	0.0534394i
$874$	−12.5917	−	21.8095i	−0.425920	−	0.737716i
$875$	2.64321	−	4.57817i	0.0893567	−	0.154770i
$876$	33.5450	+	0.415578i	1.13338	+	0.0140411i
$877$	−26.0875	+	6.99012i	−0.880912	+	0.236040i	−0.670800	−	0.741638i	$-0.734049\pi$
$877$	−26.0875	+	6.99012i	−0.880912	+	0.236040i	−0.210111	+	0.977677i	$0.567383\pi$
$878$	27.1236	−	7.26775i	0.915378	−	0.245275i
$879$	18.0025	+	0.223026i	0.607208	+	0.00752249i
$880$	−2.56940	+	4.45034i	−0.0866146	+	0.150021i
$881$	24.5324	+	42.4914i	0.826519	+	1.43157i	0.900753	+	0.434332i	$0.143016\pi$
$881$	24.5324	+	42.4914i	0.826519	+	1.43157i	−0.0742335	+	0.997241i	$0.523651\pi$
$882$	−2.35442	−	0.693818i	−0.0792775	−	0.0233621i
$883$		−	53.7025i		−	1.80723i	−0.428342	−	0.903616i	$-0.640902\pi$
$883$		−	53.7025i		−	1.80723i	0.428342	−	0.903616i	$-0.359098\pi$
$884$	−1.64776	−	7.29591i	−0.0554200	−	0.245388i
$885$	4.83630	−	4.71794i	0.162570	−	0.158592i
$886$	−6.33978	+	23.6604i	−0.212989	+	0.794886i
$887$	31.0329	−	17.9169i	1.04198	−	0.601589i	0.121589	−	0.992581i	$-0.461201\pi$
$887$	31.0329	−	17.9169i	1.04198	−	0.601589i	0.920394	+	0.390991i	$0.127868\pi$
$888$	12.2195	+	47.9734i	0.410061	+	1.60988i
$889$	−9.68603	−	9.68603i	−0.324859	−	0.324859i
$890$	−8.72462	−	32.5607i	−0.292450	−	1.09144i
$891$	−36.6936	+	7.90721i	−1.22928	+	0.264902i
$892$	−10.8594	+	10.8594i	−0.363600	+	0.363600i
$893$	13.0414	+	7.52948i	0.436415	+	0.251964i
$894$	8.71920	−	30.9992i	0.291614	−	1.03677i
$895$	6.38925	+	1.71199i	0.213569	+	0.0572257i
$896$	−8.42798			−0.281559
$897$	38.4730	+	2.00500i	1.28458	+	0.0669449i
$898$	−14.1628			−0.472619
$899$	1.10969	+	0.297339i	0.0370101	+	0.00991682i
$900$	−11.0350	+	6.01157i	−0.367832	+	0.200386i
$901$	4.85795	+	2.80474i	0.161842	+	0.0934394i
$902$	−7.53740	+	7.53740i	−0.250968	+	0.250968i
$903$	−7.87391	+	13.2560i	−0.262027	+	0.441133i
$904$	−4.44340	−	16.5830i	−0.147785	−	0.551542i
$905$	35.6799	+	35.6799i	1.18604	+	1.18604i
$906$	4.25625	−	1.08413i	0.141404	−	0.0360178i
$907$	26.4867	−	15.2921i	0.879477	−	0.507766i	0.00899086	−	0.999960i	$-0.497138\pi$
$907$	26.4867	−	15.2921i	0.879477	−	0.507766i	0.870486	+	0.492193i	$0.163805\pi$
$908$	−6.10903	+	22.7992i	−0.202735	+	0.756618i
$909$	−1.38316	+	55.8151i	−0.0458766	+	1.85127i
$910$	−7.45375	+	3.91771i	−0.247089	+	0.129871i
$911$			44.2766i			1.46695i	0.679717	+	0.733475i	$0.262103\pi$
$911$			44.2766i			1.46695i	−0.679717	+	0.733475i	$0.737897\pi$
$912$	−1.82501	−	3.25342i	−0.0604320	−	0.107732i
$913$	−9.38724	−	16.2592i	−0.310672	−	0.538100i
$914$	8.23007	−	14.2549i	0.272227	−	0.471510i
$915$	0.745512	−	60.1770i	0.0246459	−	1.98939i
$916$	−4.58719	+	1.22913i	−0.151565	+	0.0406117i
$917$	10.6559	−	2.85524i	0.351889	−	0.0942885i
$918$	−6.62360	−	0.246273i	−0.218611	−	0.00812823i
$919$	−6.93323	+	12.0087i	−0.228706	+	0.396131i	−0.957425	−	0.288682i	$-0.906783\pi$
$919$	−6.93323	+	12.0087i	−0.228706	+	0.396131i	0.728719	+	0.684813i	$0.240116\pi$
$920$	−23.9925	−	41.5563i	−0.791010	−	1.37007i
$921$	1.66202	−	0.932306i	0.0547653	−	0.0307205i
$922$			4.29778i			0.141540i
$923$	−11.1354	−	0.442076i	−0.366525	−	0.0145511i
$924$	−6.71192	−	6.88031i	−0.220806	−	0.226346i
$925$	−8.54588	+	31.8937i	−0.280987	+	1.04866i
$926$	11.4561	−	6.61417i	0.376470	−	0.217355i
$927$	0.178749	−	0.292613i	0.00587088	−	0.00961066i
$928$	0.825049	+	0.825049i	0.0270836	+	0.0270836i
$929$	−1.76962	−	6.60432i	−0.0580594	−	0.216681i	0.930801	−	0.365526i	$-0.119111\pi$
$929$	−1.76962	−	6.60432i	−0.0580594	−	0.216681i	−0.988860	+	0.148846i	$0.952444\pi$
$930$	19.8719	+	11.8037i	0.651626	+	0.387057i
$931$	3.52810	−	3.52810i	0.115629	−	0.115629i
$932$	7.81925	+	4.51445i	0.256128	+	0.147876i
$933$	−24.8117	−	6.97882i	−0.812297	−	0.228476i
$934$	16.8859	+	4.52455i	0.552522	+	0.148048i
$935$	−18.5608			−0.607003
$936$	−29.4142	−	1.89853i	−0.961434	−	0.0620555i
$937$	2.04190			0.0667058			0.0333529	−	0.999444i	$-0.489381\pi$
$937$	2.04190			0.0667058			0.0333529	+	0.999444i	$0.489381\pi$
$938$	−4.02933	−	1.07966i	−0.131562	−	0.0352520i
$939$	−17.3045	−	4.86726i	−0.564711	−	0.158837i
$940$	9.92751	+	5.73165i	0.323800	+	0.186946i
$941$	21.7751	−	21.7751i	0.709849	−	0.709849i	−0.256655	−	0.966503i	$-0.582620\pi$
$941$	21.7751	−	21.7751i	0.709849	−	0.709849i	0.966503	+	0.256655i	$0.0826203\pi$
$942$	−5.42498	−	3.22237i	−0.176755	−	0.104990i
$943$	4.98764	+	18.6141i	0.162420	+	0.606159i
$944$	0.417104	+	0.417104i	0.0135756	+	0.0135756i
$945$	−3.30390	−	14.4596i	−0.107476	−	0.470372i
$946$	26.3060	−	15.1877i	0.855280	−	0.493796i
$947$	−2.28038	+	8.51051i	−0.0741025	+	0.276554i	−0.993028	−	0.117876i	$-0.962391\pi$
$947$	−2.28038	+	8.51051i	−0.0741025	+	0.276554i	0.918926	+	0.394430i	$0.129058\pi$
$948$	−1.93559	−	1.98415i	−0.0628649	−	0.0644420i
$949$	24.4184	+	46.4578i	0.792653	+	1.50808i
$950$			12.8511i			0.416944i
$951$	−28.5456	+	16.0127i	−0.925655	+	0.519246i
$952$	−2.12424	−	3.67929i	−0.0688470	−	0.119247i
$953$	21.8599	−	37.8624i	0.708111	−	1.22648i	−0.257446	−	0.966293i	$-0.582881\pi$
$953$	21.8599	−	37.8624i	0.708111	−	1.22648i	0.965557	−	0.260191i	$-0.0837856\pi$
$954$	6.39744	−	6.08804i	0.207125	−	0.197108i
$955$	−9.15080	+	2.45195i	−0.296113	+	0.0793432i
$956$	35.5712	−	9.53127i	1.15045	−	0.308263i
$957$	−0.0179922	+	1.45231i	−0.000581606	+	0.0469467i
$958$	−10.7272	+	18.5800i	−0.346579	+	0.600293i
$959$	−10.8646	−	18.8181i	−0.350838	−	0.607669i
$960$	9.39641	+	16.7509i	0.303268	+	0.540633i
$961$			1.64780i			0.0531548i
$962$	−22.7296	+	20.9938i	−0.732831	+	0.676866i
$963$	−25.2278	−	0.625174i	−0.812955	−	0.0201459i
$964$	0.825446	−	3.08061i	0.0265858	−	0.0992197i
$965$	0.569920	−	0.329043i	0.0183464	−	0.0105923i
$966$	8.47167	−	2.15786i	0.272571	−	0.0694280i
$967$	23.4798	+	23.4798i	0.755060	+	0.755060i	0.975419	−	0.220359i	$-0.0707229\pi$
$967$	23.4798	+	23.4798i	0.755060	+	0.755060i	−0.220359	+	0.975419i	$0.570723\pi$
$968$	4.50984	+	16.8310i	0.144952	+	0.540968i
$969$	6.88081	−	11.5841i	0.221044	−	0.372135i
$970$	−3.07487	+	3.07487i	−0.0987281	+	0.0987281i
$971$	7.34396	+	4.24004i	0.235679	+	0.136069i	0.613189	−	0.789936i	$-0.289886\pi$
$971$	7.34396	+	4.24004i	0.235679	+	0.136069i	−0.377510	+	0.926005i	$0.623220\pi$
$972$	6.59827	−	19.6644i	0.211640	−	0.630735i
$973$	−8.55764	−	2.29301i	−0.274345	−	0.0735106i
$974$	−19.8184			−0.635023
$975$	−16.4909	−	10.7025i	−0.528131	−	0.342753i
$976$	5.25422			0.168184
$977$	32.0846	+	8.59705i	1.02648	+	0.275044i	0.732499	−	0.680768i	$-0.238354\pi$
$977$	32.0846	+	8.59705i	1.02648	+	0.275044i	0.293979	+	0.955812i	$0.405020\pi$
$978$	4.07116	−	14.4741i	0.130181	−	0.462832i
$979$	52.1331	+	30.0990i	1.66618	+	0.961969i
$980$	2.68569	−	2.68569i	0.0857911	−	0.0857911i
$981$	−7.50190	−	31.0555i	−0.239517	−	0.991527i
$982$	−0.164145	−	0.612599i	−0.00523809	−	0.0195488i
$983$	−29.4305	−	29.4305i	−0.938687	−	0.938687i	0.0595389	−	0.998226i	$-0.481037\pi$
$983$	−29.4305	−	29.4305i	−0.938687	−	0.938687i	−0.998226	+	0.0595389i	$0.981037\pi$
$984$	−3.63930	−	14.2878i	−0.116017	−	0.455477i
$985$	−25.0828	+	14.4815i	−0.799203	+	0.461420i
$986$	−0.0663801	+	0.247734i	−0.00211397	+	0.00788945i
$987$	−3.74196	+	3.65038i	−0.119108	+	0.116193i
$988$	12.7815	−	20.2390i	0.406633	−	0.643890i
$989$		−	54.9143i		−	1.74617i
$990$	−8.25992	+	28.0295i	−0.262518	+	0.890835i
$991$	17.3663	+	30.0793i	0.551658	+	0.955500i	0.998155	+	0.0607148i	$0.0193380\pi$
$991$	17.3663	+	30.0793i	0.551658	+	0.955500i	−0.446497	+	0.894785i	$0.647329\pi$
$992$	−16.5792	+	28.7160i	−0.526389	+	0.911732i
$993$	33.8435	+	0.419275i	1.07399	+	0.0133053i
$994$	−2.44267	+	0.654512i	−0.0774768	+	0.0207599i
$995$	46.0134	−	12.3293i	1.45872	−	0.390864i
$996$	10.3737	+	0.128517i	0.328704	+	0.00407221i
$997$	2.69355	−	4.66536i	0.0853055	−	0.147753i	−0.820216	−	0.572054i	$-0.806147\pi$
$997$	2.69355	−	4.66536i	0.0853055	−	0.147753i	0.905521	+	0.424301i	$0.139480\pi$
$998$	−5.81871	−	10.0783i	−0.184188	−	0.319023i
$999$	−25.4780	−	48.1792i	−0.806087	−	1.52432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.19	yes	112
3.2	odd	2	inner	273.2.cc.a.50.10	✓	112
13.6	odd	12	inner	273.2.cc.a.71.10	yes	112
39.32	even	12	inner	273.2.cc.a.71.19	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.10	✓	112	3.2	odd	2	inner
273.2.cc.a.50.19	yes	112	1.1	even	1	trivial
273.2.cc.a.71.10	yes	112	13.6	odd	12	inner
273.2.cc.a.71.19	yes	112	39.32	even	12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.790296 + 0.211759i) q^{2} +(1.66735 + 0.468978i) q^{3} +(-1.15232 - 0.665295i) q^{4} +(2.01842 - 2.01842i) q^{5} +(1.21839 + 0.723709i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-1.92687 - 1.92687i) q^{8} +(2.56012 + 1.56390i) q^{9} +O(q^{10})\)	\(q+(0.790296 + 0.211759i) q^{2} +(1.66735 + 0.468978i) q^{3} +(-1.15232 - 0.665295i) q^{4} +(2.01842 - 2.01842i) q^{5} +(1.21839 + 0.723709i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-1.92687 - 1.92687i) q^{8} +(2.56012 + 1.56390i) q^{9} +(2.02257 - 1.16773i) q^{10} +(-1.07945 + 4.02854i) q^{11} +(-1.60932 - 1.64970i) q^{12} +(1.07061 - 3.44294i) q^{13} -0.818175i q^{14} +(4.31201 - 2.41882i) q^{15} +(0.215825 + 0.373820i) q^{16} +(-0.779536 + 1.35020i) q^{17} +(1.69208 + 1.77808i) q^{18} +(-4.81947 + 1.29137i) q^{19} +(-3.66872 + 0.983030i) q^{20} +(0.0214561 - 1.73192i) q^{21} +(-1.70616 + 2.95516i) q^{22} +(3.08448 + 5.34248i) q^{23} +(-2.30911 - 4.11643i) q^{24} -3.14802i q^{25} +(1.57517 - 2.49423i) q^{26} +(3.53518 + 3.80822i) q^{27} +(-0.344382 + 1.28525i) q^{28} +(0.174124 - 0.100531i) q^{29} +(3.91997 - 0.998475i) q^{30} +(4.04028 + 4.04028i) q^{31} +(1.50197 + 5.60544i) q^{32} +(-3.68911 + 6.21076i) q^{33} +(-0.901981 + 0.901981i) q^{34} +(-2.47205 - 1.42724i) q^{35} +(-1.90963 - 3.50536i) q^{36} +(-10.1313 - 2.71468i) q^{37} -4.08227 q^{38} +(3.39974 - 5.23849i) q^{39} -7.77846 q^{40} +(3.01738 + 0.808505i) q^{41} +(0.383706 - 1.36418i) q^{42} +(-7.70910 - 4.45085i) q^{43} +(3.92404 - 3.92404i) q^{44} +(8.32400 - 2.01078i) q^{45} +(1.30634 + 4.87531i) q^{46} +(-2.13415 - 2.13415i) q^{47} +(0.184543 + 0.724506i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.666623 - 2.48787i) q^{50} +(-1.93297 + 1.88567i) q^{51} +(-3.52425 + 3.25511i) q^{52} -3.59796i q^{53} +(1.98741 + 3.75822i) q^{54} +(5.95252 + 10.3101i) q^{55} +(-1.36250 + 2.35992i) q^{56} +(-8.64138 - 0.107055i) q^{57} +(0.158898 - 0.0425766i) q^{58} +(1.31999 - 0.353691i) q^{59} +(-6.57806 - 0.0814933i) q^{60} +(6.08621 - 10.5416i) q^{61} +(2.33745 + 4.04859i) q^{62} +(0.848007 - 2.87765i) q^{63} +3.88471i q^{64} +(-4.78835 - 9.11021i) q^{65} +(-4.23068 + 4.12714i) q^{66} +(1.31959 - 4.92478i) q^{67} +(1.79656 - 1.03724i) q^{68} +(2.63741 + 10.3543i) q^{69} +(-1.65142 - 1.65142i) q^{70} +(-0.799966 - 2.98551i) q^{71} +(-1.91958 - 7.94645i) q^{72} +(-10.2930 + 10.2930i) q^{73} +(-7.43189 - 4.29080i) q^{74} +(1.47636 - 5.24886i) q^{75} +(6.41274 + 1.71829i) q^{76} +4.17066 q^{77} +(3.79610 - 3.42003i) q^{78} +1.20273 q^{79} +(1.19015 + 0.318900i) q^{80} +(4.10841 + 8.00755i) q^{81} +(2.21342 + 1.27792i) q^{82} +(-3.18309 + 3.18309i) q^{83} +(-1.17696 + 1.98146i) q^{84} +(1.15183 + 4.29869i) q^{85} +(-5.14996 - 5.14996i) q^{86} +(0.337473 - 0.0859595i) q^{87} +(9.84243 - 5.68253i) q^{88} +(3.73572 - 13.9419i) q^{89} +(7.00423 + 0.173573i) q^{90} +(-3.60271 - 0.143028i) q^{91} -8.20837i q^{92} +(4.84177 + 8.63138i) q^{93} +(-1.23468 - 2.13853i) q^{94} +(-7.12118 + 12.3342i) q^{95} +(-0.124514 + 10.0506i) q^{96} +(-1.79851 + 0.481910i) q^{97} +(-0.790296 + 0.211759i) q^{98} +(-9.06376 + 8.62540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

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