LMFDB - Embedded newform 272.2.l.b.69.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.14
Character	$\chi$	$=$	272.69
Dual form			272.2.l.b.205.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.27512 + 0.611614i) q^{2} +(0.148531 - 0.148531i) q^{3} +(1.25186 + 1.55976i) q^{4} +(-0.0348255 - 0.0348255i) q^{5} +(0.280239 - 0.0985512i) q^{6} +1.59619i q^{7} +(0.642295 + 2.75453i) q^{8} +2.95588i q^{9} +(-0.0231069 - 0.0657065i) q^{10} +(-2.14793 - 2.14793i) q^{11} +(0.417613 + 0.0457334i) q^{12} +(4.14741 - 4.14741i) q^{13} +(-0.976251 + 2.03533i) q^{14} -0.0103454 q^{15} +(-0.865709 + 3.90519i) q^{16} -1.00000 q^{17} +(-1.80786 + 3.76909i) q^{18} +(3.11319 - 3.11319i) q^{19} +(0.0107229 - 0.0979161i) q^{20} +(0.237084 + 0.237084i) q^{21} +(-1.42516 - 4.05257i) q^{22} -1.47961i q^{23} +(0.504535 + 0.313733i) q^{24} -4.99757i q^{25} +(7.82505 - 2.75183i) q^{26} +(0.884633 + 0.884633i) q^{27} +(-2.48967 + 1.99820i) q^{28} +(-4.28602 + 4.28602i) q^{29} +(-0.0131916 - 0.00632736i) q^{30} -10.6028 q^{31} +(-3.49235 + 4.45011i) q^{32} -0.638069 q^{33} +(-1.27512 - 0.611614i) q^{34} +(0.0555881 - 0.0555881i) q^{35} +(-4.61046 + 3.70033i) q^{36} +(5.91713 + 5.91713i) q^{37} +(5.87375 - 2.06561i) q^{38} -1.23204i q^{39} +(0.0735599 - 0.118296i) q^{40} -11.7016i q^{41} +(0.157306 + 0.447314i) q^{42} +(-8.31744 - 8.31744i) q^{43} +(0.661356 - 6.03915i) q^{44} +(0.102940 - 0.102940i) q^{45} +(0.904952 - 1.88668i) q^{46} -3.71380 q^{47} +(0.451458 + 0.708628i) q^{48} +4.45218 q^{49} +(3.05659 - 6.37250i) q^{50} +(-0.148531 + 0.148531i) q^{51} +(11.6609 + 1.27700i) q^{52} +(5.48329 + 5.48329i) q^{53} +(0.586959 + 1.66907i) q^{54} +0.149605i q^{55} +(-4.39676 + 1.02522i) q^{56} -0.924810i q^{57} +(-8.08658 + 2.84380i) q^{58} +(2.61677 + 2.61677i) q^{59} +(-0.0129509 - 0.0161363i) q^{60} +(3.06083 - 3.06083i) q^{61} +(-13.5198 - 6.48481i) q^{62} -4.71814 q^{63} +(-7.17491 + 3.53845i) q^{64} -0.288871 q^{65} +(-0.813613 - 0.390252i) q^{66} +(3.49712 - 3.49712i) q^{67} +(-1.25186 - 1.55976i) q^{68} +(-0.219769 - 0.219769i) q^{69} +(0.104880 - 0.0368830i) q^{70} +3.25952i q^{71} +(-8.14206 + 1.89854i) q^{72} +3.34201i q^{73} +(3.92605 + 11.1640i) q^{74} +(-0.742296 - 0.742296i) q^{75} +(8.75309 + 0.958563i) q^{76} +(3.42850 - 3.42850i) q^{77} +(0.753532 - 1.57100i) q^{78} +3.31001 q^{79} +(0.166149 - 0.105852i) q^{80} -8.60484 q^{81} +(7.15688 - 14.9210i) q^{82} +(-4.33884 + 4.33884i) q^{83} +(-0.0729991 + 0.666589i) q^{84} +(0.0348255 + 0.0348255i) q^{85} +(-5.51866 - 15.6928i) q^{86} +1.27322i q^{87} +(4.53694 - 7.29614i) q^{88} +9.44887i q^{89} +(0.194220 - 0.0683012i) q^{90} +(6.62005 + 6.62005i) q^{91} +(2.30784 - 1.85226i) q^{92} +(-1.57484 + 1.57484i) q^{93} +(-4.73554 - 2.27141i) q^{94} -0.216837 q^{95} +(0.142256 + 1.17970i) q^{96} +5.37018 q^{97} +(5.67706 + 2.72302i) q^{98} +(6.34901 - 6.34901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	1.27512	+	0.611614i	0.901645	+	0.432476i
$2$	1.27512	+	0.611614i	0.901645	+	0.432476i
$3$	0.148531	−	0.148531i	0.0857545	−	0.0857545i	−0.662928	−	0.748683i	$-0.730687\pi$
$3$	0.148531	−	0.148531i	0.0857545	−	0.0857545i	0.748683	+	0.662928i	$0.230687\pi$
$4$	1.25186	+	1.55976i	0.625928	+	0.779881i
$5$	−0.0348255	−	0.0348255i	−0.0155745	−	0.0155745i	0.699277	−	0.714851i	$-0.253506\pi$
$5$	−0.0348255	−	0.0348255i	−0.0155745	−	0.0155745i	−0.714851	+	0.699277i	$0.753506\pi$
$6$	0.280239	−	0.0985512i	0.114407	−	0.0402334i
$7$			1.59619i			0.603303i	0.953418	+	0.301651i	$0.0975378\pi$
$7$			1.59619i			0.603303i	−0.953418	+	0.301651i	$0.902462\pi$
$8$	0.642295	+	2.75453i	0.227085	+	0.973875i
$9$			2.95588i			0.985292i
$10$	−0.0231069	−	0.0657065i	−0.00730705	−	0.0207782i
$11$	−2.14793	−	2.14793i	−0.647625	−	0.647625i	0.304794	−	0.952418i	$-0.401412\pi$
$11$	−2.14793	−	2.14793i	−0.647625	−	0.647625i	−0.952418	+	0.304794i	$0.901412\pi$
$12$	0.417613	+	0.0457334i	0.120554	+	0.0132021i
$13$	4.14741	−	4.14741i	1.15028	−	1.15028i	0.163789	−	0.986495i	$-0.447629\pi$
$13$	4.14741	−	4.14741i	1.15028	−	1.15028i	0.986495	−	0.163789i	$-0.0523715\pi$
$14$	−0.976251	+	2.03533i	−0.260914	+	0.543965i
$15$	−0.0103454			−0.00267116
$16$	−0.865709	+	3.90519i	−0.216427	+	0.976299i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	−1.80786	+	3.76909i	−0.426116	+	0.888384i
$19$	3.11319	−	3.11319i	0.714214	−	0.714214i	−0.253200	−	0.967414i	$-0.581483\pi$
$19$	3.11319	−	3.11319i	0.714214	−	0.714214i	0.967414	+	0.253200i	$0.0814831\pi$
$20$	0.0107229	−	0.0979161i	0.00239772	−	0.0218947i
$21$	0.237084	+	0.237084i	0.0517359	+	0.0517359i
$22$	−1.42516	−	4.05257i	−0.303845	−	0.864010i
$23$		−	1.47961i		−	0.308521i	−0.988030	−	0.154260i	$-0.950701\pi$
$23$		−	1.47961i		−	0.308521i	0.988030	−	0.154260i	$-0.0492994\pi$
$24$	0.504535	+	0.313733i	0.102988	+	0.0640406i
$25$		−	4.99757i		−	0.999515i
$26$	7.82505	−	2.75183i	1.53462	−	0.539678i
$27$	0.884633	+	0.884633i	0.170248	+	0.170248i
$28$	−2.48967	+	1.99820i	−0.470504	+	0.377624i
$29$	−4.28602	+	4.28602i	−0.795895	+	0.795895i	−0.982445	−	0.186551i	$-0.940269\pi$
$29$	−4.28602	+	4.28602i	−0.795895	+	0.795895i	0.186551	+	0.982445i	$0.440269\pi$
$30$	−0.0131916	−	0.00632736i	−0.00240844	−	0.00115521i
$31$	−10.6028			−1.90432			−0.952158	−	0.305605i	$-0.901141\pi$
$31$	−10.6028			−1.90432			−0.952158	+	0.305605i	$0.901141\pi$
$32$	−3.49235	+	4.45011i	−0.617367	+	0.786675i
$33$	−0.638069			−0.111073
$34$	−1.27512	−	0.611614i	−0.218681	−	0.104891i
$35$	0.0555881	−	0.0555881i	0.00939611	−	0.00939611i
$36$	−4.61046	+	3.70033i	−0.768410	+	0.616722i
$37$	5.91713	+	5.91713i	0.972770	+	0.972770i	0.999639	−	0.0268686i	$-0.00855357\pi$
$37$	5.91713	+	5.91713i	0.972770	+	0.972770i	−0.0268686	+	0.999639i	$0.508554\pi$
$38$	5.87375	−	2.06561i	0.952848	−	0.335087i
$39$		−	1.23204i		−	0.197284i
$40$	0.0735599	−	0.118296i	0.0116308	−	0.0187043i
$41$		−	11.7016i		−	1.82749i	−0.406290	−	0.913744i	$-0.633178\pi$
$41$		−	11.7016i		−	1.82749i	0.406290	−	0.913744i	$-0.366822\pi$
$42$	0.157306	+	0.447314i	0.0242729	+	0.0690220i
$43$	−8.31744	−	8.31744i	−1.26840	−	1.26840i	−0.946916	−	0.321482i	$-0.895819\pi$
$43$	−8.31744	−	8.31744i	−1.26840	−	1.26840i	−0.321482	−	0.946916i	$-0.604181\pi$
$44$	0.661356	−	6.03915i	0.0997032	−	0.910436i
$45$	0.102940	−	0.102940i	0.0153454	−	0.0153454i
$46$	0.904952	−	1.88668i	0.133428	−	0.278176i
$47$	−3.71380			−0.541713			−0.270857	−	0.962620i	$-0.587307\pi$
$47$	−3.71380			−0.541713			−0.270857	+	0.962620i	$0.587307\pi$
$48$	0.451458	+	0.708628i	0.0651624	+	0.102282i
$49$	4.45218			0.636026
$50$	3.05659	−	6.37250i	0.432267	−	0.901208i
$51$	−0.148531	+	0.148531i	−0.0207985	+	0.0207985i
$52$	11.6609	+	1.27700i	1.61708	+	0.177089i
$53$	5.48329	+	5.48329i	0.753188	+	0.753188i	0.975073	−	0.221885i	$-0.0712210\pi$
$53$	5.48329	+	5.48329i	0.753188	+	0.753188i	−0.221885	+	0.975073i	$0.571221\pi$
$54$	0.586959	+	1.66907i	0.0798750	+	0.227131i
$55$			0.149605i			0.0201728i
$56$	−4.39676	+	1.02522i	−0.587541	+	0.137001i
$57$		−	0.924810i		−	0.122494i
$58$	−8.08658	+	2.84380i	−1.06182	+	0.373409i
$59$	2.61677	+	2.61677i	0.340675	+	0.340675i	0.856621	−	0.515946i	$-0.172560\pi$
$59$	2.61677	+	2.61677i	0.340675	+	0.340675i	−0.515946	+	0.856621i	$0.672560\pi$
$60$	−0.0129509	−	0.0161363i	−0.00167195	−	0.00208319i
$61$	3.06083	−	3.06083i	0.391899	−	0.391899i	−0.483465	−	0.875364i	$-0.660622\pi$
$61$	3.06083	−	3.06083i	0.391899	−	0.391899i	0.875364	+	0.483465i	$0.160622\pi$
$62$	−13.5198	−	6.48481i	−1.71702	−	0.823572i
$63$	−4.71814			−0.594429
$64$	−7.17491	+	3.53845i	−0.896864	+	0.442306i
$65$	−0.288871			−0.0358301
$66$	−0.813613	−	0.390252i	−0.100149	−	0.0480367i
$67$	3.49712	−	3.49712i	0.427241	−	0.427241i	−0.460447	−	0.887687i	$-0.652311\pi$
$67$	3.49712	−	3.49712i	0.427241	−	0.427241i	0.887687	+	0.460447i	$0.152311\pi$
$68$	−1.25186	−	1.55976i	−0.151810	−	0.189149i
$69$	−0.219769	−	0.219769i	−0.0264570	−	0.0264570i
$70$	0.104880	−	0.0368830i	0.0125355	−	0.00440836i
$71$			3.25952i			0.386834i	0.981117	+	0.193417i	$0.0619570\pi$
$71$			3.25952i			0.386834i	−0.981117	+	0.193417i	$0.938043\pi$
$72$	−8.14206	+	1.89854i	−0.959551	+	0.223746i
$73$			3.34201i			0.391153i	0.980688	+	0.195576i	$0.0626577\pi$
$73$			3.34201i			0.391153i	−0.980688	+	0.195576i	$0.937342\pi$
$74$	3.92605	+	11.1640i	0.456394	+	1.29779i
$75$	−0.742296	−	0.742296i	−0.0857129	−	0.0857129i
$76$	8.75309	+	0.958563i	1.00405	+	0.109955i
$77$	3.42850	−	3.42850i	0.390714	−	0.390714i
$78$	0.753532	−	1.57100i	0.0853207	−	0.177880i
$79$	3.31001			0.372405			0.186203	−	0.982511i	$-0.440382\pi$
$79$	3.31001			0.372405			0.186203	+	0.982511i	$0.440382\pi$
$80$	0.166149	−	0.105852i	0.0185761	−	0.0118346i
$81$	−8.60484			−0.956093
$82$	7.15688	−	14.9210i	0.790345	−	1.64775i
$83$	−4.33884	+	4.33884i	−0.476250	+	0.476250i	−0.903930	−	0.427680i	$-0.859331\pi$
$83$	−4.33884	+	4.33884i	−0.476250	+	0.476250i	0.427680	+	0.903930i	$0.359331\pi$
$84$	−0.0729991	+	0.666589i	−0.00796485	+	0.0727308i
$85$	0.0348255	+	0.0348255i	0.00377736	+	0.00377736i
$86$	−5.51866	−	15.6928i	−0.595093	−	1.69220i
$87$			1.27322i			0.136503i
$88$	4.53694	−	7.29614i	0.483639	−	0.777771i
$89$			9.44887i			1.00158i	0.865569	+	0.500789i	$0.166957\pi$
$89$			9.44887i			1.00158i	−0.865569	+	0.500789i	$0.833043\pi$
$90$	0.194220	−	0.0683012i	0.0204726	−	0.00719958i
$91$	6.62005	+	6.62005i	0.693969	+	0.693969i
$92$	2.30784	−	1.85226i	0.240609	−	0.193112i
$93$	−1.57484	+	1.57484i	−0.163304	+	0.163304i
$94$	−4.73554	−	2.27141i	−0.488433	−	0.234278i
$95$	−0.216837			−0.0222470
$96$	0.142256	+	1.17970i	0.0145190	+	0.120403i
$97$	5.37018			0.545259			0.272630	−	0.962119i	$-0.412107\pi$
$97$	5.37018			0.545259			0.272630	+	0.962119i	$0.412107\pi$
$98$	5.67706	+	2.72302i	0.573470	+	0.275066i
$99$	6.34901	−	6.34901i	0.638100	−	0.638100i
$100$	7.79502	−	6.25625i	0.779502	−	0.625625i
$101$	4.57814	+	4.57814i	0.455542	+	0.455542i	0.897189	−	0.441647i	$-0.145606\pi$
$101$	4.57814	+	4.57814i	0.455542	+	0.455542i	−0.441647	+	0.897189i	$0.645606\pi$
$102$	−0.280239	+	0.0985512i	−0.0277478	+	0.00975802i
$103$			11.8341i			1.16605i	0.812454	+	0.583025i	$0.198131\pi$
$103$			11.8341i			1.16605i	−0.812454	+	0.583025i	$0.801869\pi$
$104$	14.0880	+	8.76032i	1.38145	+	0.859020i
$105$		−	0.0165131i		−	0.00161152i
$106$	3.63819	+	10.3455i	0.353372	+	1.00484i
$107$	−10.2742	−	10.2742i	−0.993249	−	0.993249i	0.00672836	−	0.999977i	$-0.497858\pi$
$107$	−10.2742	−	10.2742i	−0.993249	−	0.993249i	−0.999977	+	0.00672836i	$0.997858\pi$
$108$	−0.272382	+	2.48725i	−0.0262100	+	0.239336i
$109$	−2.52970	+	2.52970i	−0.242302	+	0.242302i	−0.817802	−	0.575500i	$-0.804807\pi$
$109$	−2.52970	+	2.52970i	−0.242302	+	0.242302i	0.575500	+	0.817802i	$0.304807\pi$
$110$	−0.0915008	+	0.190765i	−0.00872426	+	0.0181887i
$111$	1.75776			0.166839
$112$	−6.23343	−	1.38183i	−0.589004	−	0.130571i
$113$	−13.1287			−1.23504			−0.617521	−	0.786555i	$-0.711863\pi$
$113$	−13.1287			−1.23504			−0.617521	+	0.786555i	$0.711863\pi$
$114$	0.565627	−	1.17924i	0.0529758	−	0.110446i
$115$	−0.0515283	+	0.0515283i	−0.00480504	+	0.00480504i
$116$	−12.0507	−	1.31969i	−1.11888	−	0.122530i
$117$	12.2592	+	12.2592i	1.13337	+	1.13337i
$118$	1.73624	+	4.93715i	0.159834	+	0.454502i
$119$		−	1.59619i		−	0.146322i
$120$	−0.00664477	−	0.0284966i	−0.000606582	−	0.00260137i
$121$		−	1.77281i		−	0.161165i
$122$	5.77496	−	2.03087i	0.522840	−	0.183867i
$123$	−1.73806	−	1.73806i	−0.156715	−	0.156715i
$124$	−13.2732	−	16.5378i	−1.19197	−	1.48514i
$125$	−0.348171	+	0.348171i	−0.0311413	+	0.0311413i
$126$	−6.01619	−	2.88568i	−0.535964	−	0.257077i
$127$	−2.18317			−0.193725			−0.0968623	−	0.995298i	$-0.530881\pi$
$127$	−2.18317			−0.193725			−0.0968623	+	0.995298i	$0.530881\pi$
$128$	−11.3130	+	0.123661i	−0.999940	+	0.0109302i
$129$	−2.47080			−0.217542
$130$	−0.368345	−	0.176678i	−0.0323060	−	0.0154957i
$131$	7.11231	−	7.11231i	0.621406	−	0.621406i	−0.324485	−	0.945891i	$-0.605191\pi$
$131$	7.11231	−	7.11231i	0.621406	−	0.621406i	0.945891	+	0.324485i	$0.105191\pi$
$132$	−0.798770	−	0.995234i	−0.0695240	−	0.0866240i
$133$	4.96923	+	4.96923i	0.430887	+	0.430887i
$134$	6.59813	−	2.32036i	0.569991	−	0.200448i
$135$		−	0.0616157i		−	0.00530303i
$136$	−0.642295	−	2.75453i	−0.0550763	−	0.236199i
$137$			10.7280i			0.916555i	0.888809	+	0.458277i	$0.151533\pi$
$137$			10.7280i			0.916555i	−0.888809	+	0.458277i	$0.848467\pi$
$138$	−0.145818	−	0.414645i	−0.0124128	−	0.0352969i
$139$	16.3996	+	16.3996i	1.39099	+	1.39099i	0.823108	+	0.567885i	$0.192238\pi$
$139$	16.3996	+	16.3996i	1.39099	+	1.39099i	0.567885	+	0.823108i	$0.307762\pi$
$140$	0.156293	+	0.0171158i	0.0132091	+	0.00144655i
$141$	−0.551615	+	0.551615i	−0.0464544	+	0.0464544i
$142$	−1.99357	+	4.15627i	−0.167296	+	0.348787i
$143$	−17.8167			−1.48990
$144$	−11.5433	−	2.55893i	−0.961940	−	0.213244i
$145$	0.298526			0.0247912
$146$	−2.04402	+	4.26146i	−0.169164	+	0.352681i
$147$	0.661288	−	0.661288i	0.0545421	−	0.0545421i
$148$	−1.82191	+	16.6367i	−0.149760	+	1.36753i
$149$	−5.91953	−	5.91953i	−0.484947	−	0.484947i	0.421760	−	0.906707i	$-0.361412\pi$
$149$	−5.91953	−	5.91953i	−0.484947	−	0.484947i	−0.906707	+	0.421760i	$0.861412\pi$
$150$	−0.492517	−	1.40051i	−0.0402138	−	0.114351i
$151$			18.5433i			1.50903i	0.656281	+	0.754516i	$0.272128\pi$
$151$			18.5433i			1.50903i	−0.656281	+	0.754516i	$0.727872\pi$
$152$	10.5750	+	6.57579i	0.857742	+	0.533367i
$153$		−	2.95588i		−	0.238968i
$154$	6.46866	−	2.27483i	0.521259	−	0.183311i
$155$	0.369248	+	0.369248i	0.0296587	+	0.0296587i
$156$	1.92169	−	1.54234i	0.153858	−	0.123486i
$157$	5.22457	−	5.22457i	0.416966	−	0.416966i	−0.467191	−	0.884157i	$-0.654734\pi$
$157$	5.22457	−	5.22457i	0.416966	−	0.416966i	0.884157	+	0.467191i	$0.154734\pi$
$158$	4.22066	+	2.02445i	0.335778	+	0.161057i
$159$	1.62888			0.129179
$160$	0.276600	−	0.0333543i	0.0218672	−	0.00263689i
$161$	2.36174			0.186131
$162$	−10.9722	−	5.26284i	−0.862057	−	0.413488i
$163$	−0.930706	+	0.930706i	−0.0728985	+	0.0728985i	−0.742616	−	0.669717i	$-0.766415\pi$
$163$	−0.930706	+	0.930706i	−0.0728985	+	0.0728985i	0.669717	+	0.742616i	$0.266415\pi$
$164$	18.2518	−	14.6488i	1.42522	−	1.14388i
$165$	0.0222211	+	0.0222211i	0.00172991	+	0.00172991i
$166$	−8.18624	+	2.87884i	−0.635375	+	0.223442i
$167$			17.5531i			1.35830i	0.733999	+	0.679150i	$0.237652\pi$
$167$			17.5531i			1.35830i	−0.733999	+	0.679150i	$0.762348\pi$
$168$	−0.500778	+	0.805333i	−0.0386358	+	0.0621328i
$169$		−	21.4020i		−	1.64631i
$170$	0.0231069	+	0.0657065i	0.00177222	+	0.00503946i
$171$	9.20219	+	9.20219i	0.703709	+	0.703709i
$172$	2.56098	−	23.3855i	0.195273	−	1.78313i
$173$	−9.64873	+	9.64873i	−0.733580	+	0.733580i	−0.971327	−	0.237747i	$-0.923591\pi$
$173$	−9.64873	+	9.64873i	−0.733580	+	0.733580i	0.237747	+	0.971327i	$0.423591\pi$
$174$	−0.778717	+	1.62350i	−0.0590344	+	0.123077i
$175$	7.97707			0.603010
$176$	10.2476	−	6.52860i	0.772439	−	0.492111i
$177$	0.777345			0.0584288
$178$	−5.77906	+	12.0484i	−0.433159	+	0.903068i
$179$	−4.32629	+	4.32629i	−0.323362	+	0.323362i	−0.850055	−	0.526693i	$-0.823432\pi$
$179$	−4.32629	+	4.32629i	−0.323362	+	0.323362i	0.526693	+	0.850055i	$0.323432\pi$
$180$	0.289428	+	0.0316957i	0.0215727	+	0.00236246i
$181$	−1.47117	−	1.47117i	−0.109351	−	0.109351i	0.650314	−	0.759665i	$-0.274637\pi$
$181$	−1.47117	−	1.47117i	−0.109351	−	0.109351i	−0.759665	+	0.650314i	$0.774637\pi$
$182$	4.39243	+	12.4903i	0.325589	+	0.925839i
$183$		−	0.909256i		−	0.0672142i
$184$	4.07564	−	0.950348i	0.300460	−	0.0700606i
$185$		−	0.412135i		−	0.0303007i
$186$	−2.97131	+	1.04492i	−0.217867	+	0.0766171i
$187$	2.14793	+	2.14793i	0.157072	+	0.157072i
$188$	−4.64914	−	5.79264i	−0.339074	−	0.422472i
$189$	−1.41204	+	1.41204i	−0.102711	+	0.102711i
$190$	−0.276493	−	0.132620i	−0.0200589	−	0.00962129i
$191$	19.5174			1.41223			0.706115	−	0.708097i	$-0.250446\pi$
$191$	19.5174			1.41223			0.706115	+	0.708097i	$0.250446\pi$
$192$	−0.540129	+	1.59127i	−0.0389805	+	0.114840i
$193$	−7.45004			−0.536265			−0.268133	−	0.963382i	$-0.586407\pi$
$193$	−7.45004			−0.536265			−0.268133	+	0.963382i	$0.586407\pi$
$194$	6.84762	+	3.28448i	0.491630	+	0.235812i
$195$	−0.0429064	+	0.0429064i	−0.00307259	+	0.00307259i
$196$	5.57349	+	6.94434i	0.398107	+	0.496024i
$197$	−11.7190	−	11.7190i	−0.834944	−	0.834944i	0.153244	−	0.988188i	$-0.451028\pi$
$197$	−11.7190	−	11.7190i	−0.834944	−	0.834944i	−0.988188	+	0.153244i	$0.951028\pi$
$198$	11.9789	−	4.21260i	0.851302	−	0.299376i
$199$		−	13.3528i		−	0.946558i	−0.880913	−	0.473279i	$-0.843070\pi$
$199$		−	13.3528i		−	0.946558i	0.880913	−	0.473279i	$-0.156930\pi$
$200$	13.7660	−	3.20992i	0.973402	−	0.226975i
$201$		−	1.03886i		−	0.0732757i
$202$	3.03762	+	8.63773i	0.213726	+	0.607749i
$203$	−6.84130	−	6.84130i	−0.480165	−	0.480165i
$204$	−0.417613	−	0.0457334i	−0.0292388	−	0.00320198i
$205$	−0.407516	+	0.407516i	−0.0284621	+	0.0284621i
$206$	−7.23791	+	15.0899i	−0.504289	+	1.05136i
$207$	4.37355			0.303983
$208$	12.6060	+	19.7869i	0.874068	+	1.37197i
$209$	−13.3738			−0.925085
$210$	0.0100997	−	0.0210562i	0.000696943	−	0.00145302i
$211$	11.9213	−	11.9213i	0.820699	−	0.820699i	−0.165509	−	0.986208i	$-0.552927\pi$
$211$	11.9213	−	11.9213i	0.820699	−	0.820699i	0.986208	+	0.165509i	$0.0529267\pi$
$212$	−1.68833	+	15.4169i	−0.115955	+	1.05884i
$213$	0.484140	+	0.484140i	0.0331727	+	0.0331727i
$214$	−6.81702	−	19.3848i	−0.466002	−	1.32511i
$215$			0.579319i			0.0395092i
$216$	−1.86856	+	3.00495i	−0.127139	+	0.204461i
$217$		−	16.9240i		−	1.14888i
$218$	−4.77287	+	1.67847i	−0.323260	+	0.113680i
$219$	0.496393	+	0.496393i	0.0335431	+	0.0335431i
$220$	−0.233349	+	0.187285i	−0.0157324	+	0.0126267i
$221$	−4.14741	+	4.14741i	−0.278985	+	0.278985i
$222$	2.24135	+	1.07507i	0.150430	+	0.0721539i
$223$	14.5496			0.974310			0.487155	−	0.873316i	$-0.338035\pi$
$223$	14.5496			0.974310			0.487155	+	0.873316i	$0.338035\pi$
$224$	−7.10321	−	5.57446i	−0.474603	−	0.372459i
$225$	14.7722			0.984814
$226$	−16.7406	−	8.02968i	−1.11357	−	0.534126i
$227$	13.6706	−	13.6706i	0.907349	−	0.907349i	−0.0887082	−	0.996058i	$-0.528274\pi$
$227$	13.6706	−	13.6706i	0.907349	−	0.907349i	0.996058	+	0.0887082i	$0.0282739\pi$
$228$	1.44248	−	1.15773i	0.0955308	−	0.0766725i
$229$	5.30652	+	5.30652i	0.350665	+	0.350665i	0.860357	−	0.509692i	$-0.170241\pi$
$229$	5.30652	+	5.30652i	0.350665	+	0.350665i	−0.509692	+	0.860357i	$0.670241\pi$
$230$	−0.0972202	+	0.0341893i	−0.00641051	+	0.00225438i
$231$		−	1.01848i		−	0.0670109i
$232$	−14.5589	−	9.05311i	−0.955838	−	0.594366i
$233$			16.4401i			1.07703i	0.842616	+	0.538515i	$0.181014\pi$
$233$			16.4401i			1.07703i	−0.842616	+	0.538515i	$0.818986\pi$
$234$	8.13406	+	23.1299i	0.531740	+	1.51205i
$235$	0.129335	+	0.129335i	0.00843689	+	0.00843689i
$236$	−0.805715	+	7.35736i	−0.0524476	+	0.478924i
$237$	0.491640	−	0.491640i	0.0319354	−	0.0319354i
$238$	0.976251	−	2.03533i	0.0632810	−	0.131931i
$239$	−15.9200			−1.02978			−0.514889	−	0.857257i	$-0.672167\pi$
$239$	−15.9200			−1.02978			−0.514889	+	0.857257i	$0.672167\pi$
$240$	0.00895607	−	0.0404006i	0.000578112	−	0.00260785i
$241$	−4.48670			−0.289014			−0.144507	−	0.989504i	$-0.546160\pi$
$241$	−4.48670			−0.289014			−0.144507	+	0.989504i	$0.546160\pi$
$242$	1.08428	−	2.26055i	0.0696999	−	0.145313i
$243$	−3.93199	+	3.93199i	−0.252237	+	0.252237i
$244$	8.60587	+	0.942441i	0.550935	+	0.0603336i
$245$	−0.155050	−	0.155050i	−0.00990576	−	0.00990576i
$246$	−1.15321	−	3.27925i	−0.0735260	−	0.209077i
$247$		−	25.8233i		−	1.64310i
$248$	−6.81012	−	29.2057i	−0.432443	−	1.85457i
$249$			1.28891i			0.0816812i
$250$	−0.656905	+	0.231013i	−0.0415463	+	0.0146106i
$251$	−6.12949	−	6.12949i	−0.386890	−	0.386890i	0.486687	−	0.873577i	$-0.338205\pi$
$251$	−6.12949	−	6.12949i	−0.386890	−	0.386890i	−0.873577	+	0.486687i	$0.838205\pi$
$252$	−5.90643	−	7.35917i	−0.372070	−	0.463584i
$253$	−3.17810	+	3.17810i	−0.199806	+	0.199806i
$254$	−2.78380	−	1.33525i	−0.174671	−	0.0837813i
$255$	0.0103454			0.000647851
$256$	−14.5011	−	6.76153i	−0.906318	−	0.422595i
$257$	−25.8986			−1.61551			−0.807755	−	0.589518i	$-0.799318\pi$
$257$	−25.8986			−1.61551			−0.807755	+	0.589518i	$0.799318\pi$
$258$	−3.15056	−	1.51117i	−0.196145	−	0.0940816i
$259$	−9.44486	+	9.44486i	−0.586875	+	0.586875i
$260$	−0.361626	−	0.450570i	−0.0224271	−	0.0279432i
$261$	−12.6690	−	12.6690i	−0.784189	−	0.784189i
$262$	13.4190	−	4.71905i	0.829031	−	0.291544i
$263$		−	9.42469i		−	0.581152i	−0.956852	−	0.290576i	$-0.906153\pi$
$263$		−	9.42469i		−	0.581152i	0.956852	−	0.290576i	$-0.0938468\pi$
$264$	−0.409828	−	1.75758i	−0.0252232	−	0.108172i
$265$		−	0.381917i		−	0.0234610i
$266$	3.29711	+	9.37561i	0.202159	+	0.574856i
$267$	1.40345	+	1.40345i	0.0858898	+	0.0858898i
$268$	9.83256	+	1.07678i	0.600619	+	0.0657746i
$269$	5.35879	−	5.35879i	0.326731	−	0.326731i	−0.524611	−	0.851342i	$-0.675789\pi$
$269$	5.35879	−	5.35879i	0.326731	−	0.326731i	0.851342	+	0.524611i	$0.175789\pi$
$270$	0.0376850	−	0.0785673i	0.00229344	−	0.00478145i
$271$	−17.4267			−1.05859			−0.529297	−	0.848437i	$-0.677544\pi$
$271$	−17.4267			−1.05859			−0.529297	+	0.848437i	$0.677544\pi$
$272$	0.865709	−	3.90519i	0.0524913	−	0.236787i
$273$	1.96657			0.119022
$274$	−6.56139	+	13.6795i	−0.396388	+	0.826407i
$275$	−10.7344	+	10.7344i	−0.647310	+	0.647310i
$276$	0.0676677	−	0.617905i	0.00407312	−	0.0371935i
$277$	−18.7059	−	18.7059i	−1.12393	−	1.12393i	−0.991145	−	0.132787i	$-0.957607\pi$
$277$	−18.7059	−	18.7059i	−1.12393	−	1.12393i	−0.132787	−	0.991145i	$-0.542393\pi$
$278$	10.8812	+	30.9416i	0.652611	+	1.85575i
$279$		−	31.3405i		−	1.87631i
$280$	0.188823	+	0.117415i	0.0112844	+	0.00701691i
$281$		−	4.90274i		−	0.292473i	−0.989250	−	0.146237i	$-0.953284\pi$
$281$		−	4.90274i		−	0.292473i	0.989250	−	0.146237i	$-0.0467161\pi$
$282$	−1.04075	+	0.365999i	−0.0619758	+	0.0217949i
$283$	9.42568	+	9.42568i	0.560298	+	0.560298i	0.929392	−	0.369094i	$-0.120332\pi$
$283$	9.42568	+	9.42568i	0.560298	+	0.560298i	−0.369094	+	0.929392i	$0.620332\pi$
$284$	−5.08407	+	4.08045i	−0.301684	+	0.242130i
$285$	−0.0322070	+	0.0322070i	−0.00190778	+	0.00190778i
$286$	−22.7184	−	10.8969i	−1.34337	−	0.644348i
$287$	18.6780			1.10253
$288$	−13.1540	−	10.3230i	−0.775105	−	0.608287i
$289$	1.00000			0.0588235
$290$	0.380656	+	0.182583i	0.0223529	+	0.0107216i
$291$	0.797639	−	0.797639i	0.0467584	−	0.0467584i
$292$	−5.21274	+	4.18372i	−0.305052	+	0.244834i
$293$	−12.8126	−	12.8126i	−0.748517	−	0.748517i	0.225683	−	0.974201i	$-0.427539\pi$
$293$	−12.8126	−	12.8126i	−0.748517	−	0.748517i	−0.974201	+	0.225683i	$0.927539\pi$
$294$	1.24767	−	0.438768i	0.0727658	−	0.0255895i
$295$		−	0.182261i		−	0.0106116i
$296$	−12.4984	+	20.0995i	−0.726455	+	1.16826i
$297$		−	3.80026i		−	0.220513i
$298$	−3.92764	−	11.1686i	−0.227522	−	0.646979i
$299$	−6.13656	−	6.13656i	−0.354886	−	0.354886i
$300$	0.228556	−	2.08705i	0.0131957	−	0.120496i
$301$	13.2762	−	13.2762i	0.765228	−	0.765228i
$302$	−11.3413	+	23.6449i	−0.652621	+	1.36061i
$303$	1.35999			0.0781296
$304$	9.46248	+	14.8527i	0.542711	+	0.851861i
$305$	−0.213190			−0.0122072
$306$	1.80786	−	3.76909i	0.103348	−	0.215465i
$307$	8.43062	−	8.43062i	0.481161	−	0.481161i	−0.424341	−	0.905502i	$-0.639494\pi$
$307$	8.43062	−	8.43062i	0.481161	−	0.481161i	0.905502	+	0.424341i	$0.139494\pi$
$308$	9.63963	+	1.05565i	0.549269	+	0.0601512i
$309$	1.75774	+	1.75774i	0.0999941	+	0.0999941i
$310$	0.244998	+	0.696672i	0.0139149	+	0.0395683i
$311$			18.0067i			1.02107i	0.859857	+	0.510534i	$0.170552\pi$
$311$			18.0067i			1.02107i	−0.859857	+	0.510534i	$0.829448\pi$
$312$	3.39369	−	0.791332i	0.192130	−	0.0448004i
$313$		−	7.22986i		−	0.408656i	−0.978902	−	0.204328i	$-0.934499\pi$
$313$		−	7.22986i		−	0.408656i	0.978902	−	0.204328i	$-0.0655009\pi$
$314$	9.85737	−	3.46653i	0.556283	−	0.195627i
$315$	0.164312	+	0.164312i	0.00925791	+	0.00925791i
$316$	4.14366	+	5.16283i	0.233099	+	0.290432i
$317$	6.51893	−	6.51893i	0.366140	−	0.366140i	−0.499928	−	0.866067i	$-0.666640\pi$
$317$	6.51893	−	6.51893i	0.366140	−	0.366140i	0.866067	+	0.499928i	$0.166640\pi$
$318$	2.07701	+	0.996245i	0.116473	+	0.0558666i
$319$	18.4121			1.03088
$320$	0.373098	+	0.126642i	0.0208568	+	0.00707950i
$321$	−3.05209			−0.170351
$322$	3.01150	+	1.44447i	0.167824	+	0.0804974i
$323$	−3.11319	+	3.11319i	−0.173222	+	0.173222i
$324$	−10.7720	−	13.4215i	−0.598446	−	0.745639i
$325$	−20.7270	−	20.7270i	−1.14973	−	1.14973i
$326$	−1.75599	+	0.617528i	−0.0972555	+	0.0342017i
$327$			0.751479i			0.0415569i
$328$	32.2325	−	7.51590i	1.77974	−	0.414996i
$329$		−	5.92792i		−	0.326817i
$330$	0.0147438	+	0.0419252i	0.000811619	+	0.00230791i
$331$	−12.8703	−	12.8703i	−0.707413	−	0.707413i	0.258577	−	0.965991i	$-0.416746\pi$
$331$	−12.8703	−	12.8703i	−0.707413	−	0.707413i	−0.965991	+	0.258577i	$0.916746\pi$
$332$	−12.1992	−	1.33595i	−0.669516	−	0.0733197i
$333$	−17.4903	+	17.4903i	−0.958463	+	0.958463i
$334$	−10.7357	+	22.3823i	−0.587433	+	1.22471i
$335$	−0.243578			−0.0133081
$336$	−1.13110	+	0.720613i	−0.0617068	+	0.0393126i
$337$	13.0539			0.711094			0.355547	−	0.934658i	$-0.384295\pi$
$337$	13.0539			0.711094			0.355547	+	0.934658i	$0.384295\pi$
$338$	13.0898	−	27.2901i	0.711989	−	1.48438i
$339$	−1.95002	+	1.95002i	−0.105910	+	0.105910i
$340$	−0.0107229	+	0.0979161i	−0.000581533	+	0.00531025i
$341$	22.7740	+	22.7740i	1.23328	+	1.23328i
$342$	6.10570	+	17.3621i	0.330159	+	0.938834i
$343$			18.2798i			0.987019i
$344$	17.5684	−	28.2529i	0.947226	−	1.52330i
$345$			0.0153071i			0.000824108i
$346$	−18.2046	+	6.40198i	−0.978684	+	0.344173i
$347$	−5.32564	−	5.32564i	−0.285895	−	0.285895i	0.549559	−	0.835455i	$-0.314796\pi$
$347$	−5.32564	−	5.32564i	−0.285895	−	0.285895i	−0.835455	+	0.549559i	$0.814796\pi$
$348$	−1.98591	+	1.59388i	−0.106456	+	0.0854412i
$349$	10.0817	−	10.0817i	0.539664	−	0.539664i	−0.383767	−	0.923430i	$-0.625373\pi$
$349$	10.0817	−	10.0817i	0.539664	−	0.539664i	0.923430	+	0.383767i	$0.125373\pi$
$350$	10.1717	+	4.87889i	0.543701	+	0.260788i
$351$	7.33787			0.391667
$352$	17.0598	−	2.05719i	0.909292	−	0.109648i
$353$	−9.14212			−0.486586			−0.243293	−	0.969953i	$-0.578228\pi$
$353$	−9.14212			−0.486586			−0.243293	+	0.969953i	$0.578228\pi$
$354$	0.991207	+	0.475435i	0.0526820	+	0.0252691i
$355$	0.113514	−	0.113514i	0.00602472	−	0.00602472i
$356$	−14.7380	+	11.8286i	−0.781111	+	0.626916i
$357$	−0.237084	−	0.237084i	−0.0125478	−	0.0125478i
$358$	−8.16256	+	2.87052i	−0.431405	+	0.151712i
$359$			14.5754i			0.769259i	0.923071	+	0.384629i	$0.125671\pi$
$359$			14.5754i			0.769259i	−0.923071	+	0.384629i	$0.874329\pi$
$360$	0.349670	+	0.217434i	0.0184292	+	0.0114598i
$361$		−	0.383851i		−	0.0202027i
$362$	−0.976128	−	2.77570i	−0.0513041	−	0.145888i
$363$	−0.263318	−	0.263318i	−0.0138206	−	0.0138206i
$364$	−2.03834	+	18.6130i	−0.106838	+	0.975588i
$365$	0.116387	−	0.116387i	0.00609199	−	0.00609199i
$366$	0.556114	−	1.15941i	0.0290685	−	0.0606033i
$367$	4.22574			0.220582			0.110291	−	0.993899i	$-0.464822\pi$
$367$	4.22574			0.220582			0.110291	+	0.993899i	$0.464822\pi$
$368$	5.77818	+	1.28091i	0.301208	+	0.0667723i
$369$	34.5886			1.80061
$370$	0.252067	−	0.525521i	0.0131043	−	0.0273205i
$371$	−8.75236	+	8.75236i	−0.454400	+	0.454400i
$372$	−4.42786	−	0.484901i	−0.229574	−	0.0251410i
$373$	−9.29891	−	9.29891i	−0.481479	−	0.481479i	0.424124	−	0.905604i	$-0.360582\pi$
$373$	−9.29891	−	9.29891i	−0.481479	−	0.481479i	−0.905604	+	0.424124i	$0.860582\pi$
$374$	1.42516	+	4.05257i	0.0736933	+	0.209553i
$375$			0.103428i			0.00534102i
$376$	−2.38535	−	10.2298i	−0.123015	−	0.527561i
$377$			35.5518i			1.83101i
$378$	−2.66415	+	0.936897i	−0.137029	+	0.0481888i
$379$	24.9361	+	24.9361i	1.28088	+	1.28088i	0.940166	+	0.340718i	$0.110670\pi$
$379$	24.9361	+	24.9361i	1.28088	+	1.28088i	0.340718	+	0.940166i	$0.389330\pi$
$380$	−0.271449	−	0.338213i	−0.0139250	−	0.0173500i
$381$	−0.324268	+	0.324268i	−0.0166128	+	0.0166128i
$382$	24.8870	+	11.9371i	1.27333	+	0.610756i
$383$	−15.3891			−0.786349			−0.393174	−	0.919464i	$-0.628623\pi$
$383$	−15.3891			−0.786349			−0.393174	+	0.919464i	$0.628623\pi$
$384$	−1.66197	+	1.69871i	−0.0848121	+	0.0866867i
$385$	−0.238799			−0.0121703
$386$	−9.49968	−	4.55655i	−0.483521	−	0.231922i
$387$	24.5853	−	24.5853i	1.24974	−	1.24974i
$388$	6.72269	+	8.37620i	0.341293	+	0.425237i
$389$	15.7490	+	15.7490i	0.798506	+	0.798506i	0.982860	−	0.184354i	$-0.0590193\pi$
$389$	15.7490	+	15.7490i	0.798506	+	0.798506i	−0.184354	+	0.982860i	$0.559019\pi$
$390$	−0.0809529	+	0.0284686i	−0.00409921	+	0.00144156i
$391$			1.47961i			0.0748272i
$392$	2.85961	+	12.2637i	0.144432	+	0.619410i
$393$		−	2.11280i		−	0.106577i
$394$	−7.77562	−	22.1106i	−0.391730	−	1.11392i
$395$	−0.115273	−	0.115273i	−0.00580001	−	0.00580001i
$396$	17.8510	+	1.95489i	0.897046	+	0.0982368i
$397$	−11.3229	+	11.3229i	−0.568278	+	0.568278i	−0.931646	−	0.363368i	$-0.881627\pi$
$397$	−11.3229	+	11.3229i	−0.568278	+	0.568278i	0.363368	+	0.931646i	$0.381627\pi$
$398$	8.16679	−	17.0265i	0.409364	−	0.853460i
$399$	1.47617			0.0739010
$400$	19.5165	+	4.32645i	0.975825	+	0.216322i
$401$	10.8934			0.543990			0.271995	−	0.962299i	$-0.412317\pi$
$401$	10.8934			0.543990			0.271995	+	0.962299i	$0.412317\pi$
$402$	0.635382	−	1.32467i	0.0316900	−	0.0660687i
$403$	−43.9741	+	43.9741i	−2.19051	+	2.19051i
$404$	−1.40963	+	12.8720i	−0.0701317	+	0.640405i
$405$	0.299668	+	0.299668i	0.0148906	+	0.0148906i
$406$	−4.53924	−	12.9077i	−0.225279	−	0.640599i
$407$		−	25.4191i		−	1.25998i
$408$	−0.504535	−	0.313733i	−0.0249782	−	0.0155321i
$409$		−	4.43537i		−	0.219315i	−0.993969	−	0.109658i	$-0.965025\pi$
$409$		−	4.43537i		−	0.219315i	0.993969	−	0.109658i	$-0.0349754\pi$
$410$	−0.768873	+	0.270389i	−0.0379719	+	0.0133535i
$411$	1.59344	+	1.59344i	0.0785987	+	0.0785987i
$412$	−18.4584	+	14.8146i	−0.909380	+	0.729864i
$413$	−4.17686	+	4.17686i	−0.205530	+	0.205530i
$414$	5.57680	+	2.67493i	0.274085	+	0.131465i
$415$	0.302205			0.0148347
$416$	3.97220	+	32.9406i	0.194753	+	1.61505i
$417$	4.87169			0.238568
$418$	−17.0532	−	8.17960i	−0.834098	−	0.400077i
$419$	9.14441	−	9.14441i	0.446734	−	0.446734i	−0.447533	−	0.894267i	$-0.647697\pi$
$419$	9.14441	−	9.14441i	0.446734	−	0.446734i	0.894267	+	0.447533i	$0.147697\pi$
$420$	0.0257565	−	0.0206721i	0.00125679	−	0.00100869i
$421$	−1.06858	−	1.06858i	−0.0520794	−	0.0520794i	0.680587	−	0.732667i	$-0.261725\pi$
$421$	−1.06858	−	1.06858i	−0.0520794	−	0.0520794i	−0.732667	+	0.680587i	$0.761725\pi$
$422$	22.4924	−	7.90987i	1.09491	−	0.385047i
$423$		−	10.9775i		−	0.533746i
$424$	−11.5820	+	18.6258i	−0.562473	+	0.904549i
$425$			4.99757i			0.242418i
$426$	0.321229	+	0.913443i	0.0155636	+	0.0442565i
$427$	4.88566	+	4.88566i	0.236433	+	0.236433i
$428$	3.16348	−	28.8873i	0.152913	−	1.39632i
$429$	−2.64633	+	2.64633i	−0.127766	+	0.127766i
$430$	−0.354319	+	0.738700i	−0.0170868	+	0.0356233i
$431$	30.9487			1.49075			0.745373	−	0.666648i	$-0.232272\pi$
$431$	30.9487			1.49075			0.745373	+	0.666648i	$0.232272\pi$
$432$	−4.22050	+	2.68883i	−0.203059	+	0.129366i
$433$	6.51895			0.313281			0.156640	−	0.987656i	$-0.449934\pi$
$433$	6.51895			0.313281			0.156640	+	0.987656i	$0.449934\pi$
$434$	10.3510	−	21.5802i	0.496863	−	1.03588i
$435$	0.0443404	−	0.0443404i	0.00212596	−	0.00212596i
$436$	−7.11256	−	0.778906i	−0.340630	−	0.0373028i
$437$	−4.60631	−	4.60631i	−0.220350	−	0.220350i
$438$	0.329359	+	0.936560i	0.0157374	+	0.0447506i
$439$		−	19.4763i		−	0.929555i	−0.885428	−	0.464777i	$-0.846134\pi$
$439$		−	19.4763i		−	0.929555i	0.885428	−	0.464777i	$-0.153866\pi$
$440$	−0.412093	+	0.0960908i	−0.0196458	+	0.00458095i
$441$			13.1601i			0.626672i
$442$	−7.82505	+	2.75183i	−0.372200	+	0.130891i
$443$	−6.49212	−	6.49212i	−0.308450	−	0.308450i	0.535858	−	0.844308i	$-0.319988\pi$
$443$	−6.49212	−	6.49212i	−0.308450	−	0.308450i	−0.844308	+	0.535858i	$0.819988\pi$
$444$	2.20046	+	2.74168i	0.104429	+	0.130114i
$445$	0.329062	−	0.329062i	0.0155990	−	0.0155990i
$446$	18.5524	+	8.89871i	0.878482	+	0.421366i
$447$	−1.75847			−0.0831728
$448$	−5.64803	−	11.4525i	−0.266844	−	0.541081i
$449$	−3.81772			−0.180169			−0.0900846	−	0.995934i	$-0.528714\pi$
$449$	−3.81772			−0.180169			−0.0900846	+	0.995934i	$0.528714\pi$
$450$	18.8363	+	9.03489i	0.887953	+	0.425909i
$451$	−25.1343	+	25.1343i	−1.18353	+	1.18353i
$452$	−16.4352	−	20.4776i	−0.773047	−	0.963185i
$453$	2.75426	+	2.75426i	0.129406	+	0.129406i
$454$	25.7928	−	9.07051i	1.21051	−	0.425700i
$455$		−	0.461093i		−	0.0216164i
$456$	2.54742	−	0.594001i	0.119294	−	0.0278166i
$457$			33.4532i			1.56488i	0.622729	+	0.782438i	$0.286024\pi$
$457$			33.4532i			1.56488i	−0.622729	+	0.782438i	$0.713976\pi$
$458$	3.52091	+	10.0120i	0.164521	+	0.467830i
$459$	−0.884633	−	0.884633i	−0.0412912	−	0.0412912i
$460$	−0.144878	−	0.0158658i	−0.00675497	−	0.000739746i
$461$	7.53201	−	7.53201i	0.350801	−	0.350801i	−0.509607	−	0.860407i	$-0.670209\pi$
$461$	7.53201	−	7.53201i	0.350801	−	0.350801i	0.860407	+	0.509607i	$0.170209\pi$
$462$	0.622915	−	1.29868i	0.0289806	−	0.0604201i
$463$	−32.8432			−1.52635			−0.763177	−	0.646189i	$-0.776362\pi$
$463$	−32.8432			−1.52635			−0.763177	+	0.646189i	$0.776362\pi$
$464$	−13.0273	−	20.4482i	−0.604778	−	0.949284i
$465$	0.109690			0.00508673
$466$	−10.0550	+	20.9631i	−0.465790	+	0.971099i
$467$	−5.46664	+	5.46664i	−0.252966	+	0.252966i	−0.822186	−	0.569220i	$-0.807245\pi$
$467$	−5.46664	+	5.46664i	−0.252966	+	0.252966i	0.569220	+	0.822186i	$0.307245\pi$
$468$	−3.77467	+	34.4683i	−0.174484	+	1.59330i
$469$	5.58206	+	5.58206i	0.257756	+	0.257756i
$470$	0.0858144	+	0.244021i	0.00395832	+	0.0112558i
$471$		−	1.55202i		−	0.0715134i
$472$	−5.52725	+	8.88873i	−0.254412	+	0.409137i
$473$			35.7305i			1.64289i
$474$	0.927593	−	0.326206i	0.0426058	−	0.0149831i
$475$	−15.5584	−	15.5584i	−0.713867	−	0.713867i
$476$	2.48967	−	1.99820i	0.114114	−	0.0915873i
$477$	−16.2079	+	16.2079i	−0.742110	+	0.742110i
$478$	−20.2999	−	9.73689i	−0.928495	−	0.445355i
$479$	41.3124			1.88761			0.943807	−	0.330498i	$-0.107217\pi$
$479$	41.3124			1.88761			0.943807	+	0.330498i	$0.107217\pi$
$480$	0.0361296	−	0.0460380i	0.00164908	−	0.00210134i
$481$	49.0815			2.23792
$482$	−5.72107	−	2.74413i	−0.260588	−	0.124992i
$483$	0.350792	−	0.350792i	0.0159616	−	0.0159616i
$484$	2.76516	−	2.21931i	0.125689	−	0.100878i
$485$	−0.187019	−	0.187019i	−0.00849211	−	0.00849211i
$486$	−7.41861	+	2.60889i	−0.336515	+	0.118342i
$487$			29.8216i			1.35135i	0.737201	+	0.675673i	$0.236147\pi$
$487$			29.8216i			1.35135i	−0.737201	+	0.675673i	$0.763853\pi$
$488$	10.3971	+	6.46520i	0.470655	+	0.292666i
$489$			0.276478i			0.0125028i
$490$	−0.102876	−	0.292537i	−0.00464747	−	0.0132155i
$491$	−2.65242	−	2.65242i	−0.119702	−	0.119702i	0.644718	−	0.764420i	$-0.276975\pi$
$491$	−2.65242	−	2.65242i	−0.119702	−	0.119702i	−0.764420	+	0.644718i	$0.776975\pi$
$492$	0.535155	−	4.88675i	0.0241267	−	0.220312i
$493$	4.28602	−	4.28602i	0.193033	−	0.193033i
$494$	15.7939	−	32.9278i	0.710601	−	1.48149i
$495$	−0.442215			−0.0198761
$496$	9.17893	−	41.4060i	0.412146	−	1.85918i
$497$	−5.20281			−0.233378
$498$	−0.788313	+	1.64351i	−0.0353252	+	0.0736474i
$499$	−11.5684	+	11.5684i	−0.517871	+	0.517871i	−0.916927	−	0.399056i	$-0.869338\pi$
$499$	−11.5684	+	11.5684i	−0.517871	+	0.517871i	0.399056	+	0.916927i	$0.369338\pi$
$500$	−0.978923	−	0.107203i	−0.0437788	−	0.00479428i
$501$	2.60718	+	2.60718i	0.116480	+	0.116480i
$502$	−4.06695	−	11.5647i	−0.181517	−	0.516158i
$503$		−	16.7898i		−	0.748618i	−0.927304	−	0.374309i	$-0.877880\pi$
$503$		−	16.7898i		−	0.748618i	0.927304	−	0.374309i	$-0.122120\pi$
$504$	−3.03043	−	12.9963i	−0.134986	−	0.578900i
$505$		−	0.318872i		−	0.0141896i
$506$	−5.99623	+	2.10869i	−0.266565	+	0.0937426i
$507$	−3.17886	−	3.17886i	−0.141178	−	0.141178i
$508$	−2.73301	−	3.40522i	−0.121258	−	0.151082i
$509$	19.1676	−	19.1676i	0.849591	−	0.849591i	−0.140491	−	0.990082i	$-0.544868\pi$
$509$	19.1676	−	19.1676i	0.849591	−	0.849591i	0.990082	+	0.140491i	$0.0448681\pi$
$510$	0.0131916	+	0.00632736i	0.000584132	+	0.000280180i
$511$	−5.33448			−0.235983
$512$	−14.3552	−	17.4908i	−0.634415	−	0.772992i
$513$	5.50806			0.243187
$514$	−33.0238	−	15.8399i	−1.45662	−	0.698670i
$515$	0.412129	−	0.412129i	0.0181606	−	0.0181606i
$516$	−3.09309	−	3.85386i	−0.136166	−	0.169657i
$517$	7.97697	+	7.97697i	0.350827	+	0.350827i
$518$	−17.8199	+	6.26671i	−0.782962	+	0.275343i
$519$			2.86628i			0.125816i
$520$	−0.185541	−	0.795706i	−0.00813649	−	0.0348940i
$521$		−	20.8283i		−	0.912504i	−0.889851	−	0.456252i	$-0.849191\pi$
$521$		−	20.8283i		−	0.912504i	0.889851	−	0.456252i	$-0.150809\pi$
$522$	−8.40592	−	23.9029i	−0.367917	−	1.04620i
$523$	10.4490	+	10.4490i	0.456904	+	0.456904i	0.897638	−	0.440734i	$-0.145282\pi$
$523$	10.4490	+	10.4490i	0.456904	+	0.456904i	−0.440734	+	0.897638i	$0.645282\pi$
$524$	19.9971	+	2.18991i	0.873577	+	0.0956667i
$525$	1.18484	−	1.18484i	0.0517108	−	0.0517108i
$526$	5.76427	−	12.0176i	0.251334	−	0.523993i
$527$	10.6028			0.461865
$528$	0.552382	−	2.49178i	0.0240393	−	0.108441i
$529$	20.8107			0.904815
$530$	0.233586	−	0.486990i	0.0101463	−	0.0211535i
$531$	−7.73486	+	7.73486i	−0.335664	+	0.335664i
$532$	−1.53005	+	13.9716i	−0.0663360	+	0.605745i
$533$	−48.5315	−	48.5315i	−2.10213	−	2.10213i
$534$	0.931197	+	2.64794i	0.0402968	+	0.114587i
$535$			0.715612i			0.0309386i
$536$	11.8791	+	7.38675i	0.513099	+	0.319059i
$537$			1.28518i			0.0554595i
$538$	10.1106	−	3.55558i	0.435899	−	0.153292i
$539$	−9.56297	−	9.56297i	−0.411906	−	0.411906i
$540$	0.0961057	−	0.0771340i	0.00413573	−	0.00331932i
$541$	−2.29092	+	2.29092i	−0.0984945	+	0.0984945i	−0.754637	−	0.656143i	$-0.772187\pi$
$541$	−2.29092	+	2.29092i	−0.0984945	+	0.0984945i	0.656143	+	0.754637i	$0.272187\pi$
$542$	−22.2211	−	10.6584i	−0.954476	−	0.457817i
$543$	−0.437029			−0.0187547
$544$	3.49235	−	4.45011i	0.149733	−	0.190797i
$545$	0.176196			0.00754743
$546$	2.50761	+	1.20278i	0.107316	+	0.0514742i
$547$	−7.84902	+	7.84902i	−0.335600	+	0.335600i	−0.854708	−	0.519108i	$-0.826264\pi$
$547$	−7.84902	+	7.84902i	−0.335600	+	0.335600i	0.519108	+	0.854708i	$0.326264\pi$
$548$	−16.7331	+	13.4299i	−0.714803	+	0.573698i
$549$	9.04743	+	9.04743i	0.386135	+	0.386135i
$550$	−20.2530	+	7.12235i	−0.863591	+	0.303698i
$551$			26.6864i			1.13688i
$552$	0.464204	−	0.746516i	0.0197578	−	0.0317739i
$553$			5.28340i			0.224673i
$554$	−12.4115	−	35.2931i	−0.527314	−	1.49946i
$555$	−0.0612148	−	0.0612148i	−0.00259842	−	0.00259842i
$556$	−5.04950	+	46.1093i	−0.214146	+	1.95547i
$557$	3.42568	−	3.42568i	0.145151	−	0.145151i	−0.630797	−	0.775948i	$-0.717272\pi$
$557$	3.42568	−	3.42568i	0.145151	−	0.145151i	0.775948	+	0.630797i	$0.217272\pi$
$558$	19.1683	−	39.9629i	0.811459	−	1.69177i
$559$	−68.9916			−2.91804
$560$	0.168959	+	0.265206i	0.00713983	+	0.0112070i
$561$	0.638069			0.0269393
$562$	2.99859	−	6.25158i	0.126488	−	0.263707i
$563$	11.5463	−	11.5463i	0.486620	−	0.486620i	−0.420618	−	0.907238i	$-0.638187\pi$
$563$	11.5463	−	11.5463i	0.486620	−	0.486620i	0.907238	+	0.420618i	$0.138187\pi$
$564$	−1.55093	−	0.169845i	−0.0653059	−	0.00715175i
$565$	0.457213	+	0.457213i	0.0192351	+	0.0192351i
$566$	6.25399	+	17.7837i	0.262875	+	0.747506i
$567$		−	13.7349i		−	0.576814i
$568$	−8.97845	+	2.09357i	−0.376728	+	0.0878443i
$569$			0.574149i			0.0240696i	0.999928	+	0.0120348i	$0.00383089\pi$
$569$			0.574149i			0.0240696i	−0.999928	+	0.0120348i	$0.996169\pi$
$570$	−0.0607660	+	0.0213695i	−0.00254521	+	0.000895070i
$571$	24.2042	+	24.2042i	1.01291	+	1.01291i	0.999916	+	0.0129991i	$0.00413785\pi$
$571$	24.2042	+	24.2042i	1.01291	+	1.01291i	0.0129991	+	0.999916i	$0.495862\pi$
$572$	−22.3039	−	27.7897i	−0.932574	−	1.16195i
$573$	2.89894	−	2.89894i	0.121105	−	0.121105i
$574$	23.8167	+	11.4237i	0.994090	+	0.476817i
$575$	−7.39448			−0.308371
$576$	−10.4592	−	21.2082i	−0.435800	−	0.883674i
$577$	8.95062			0.372619			0.186310	−	0.982491i	$-0.440347\pi$
$577$	8.95062			0.372619			0.186310	+	0.982491i	$0.440347\pi$
$578$	1.27512	+	0.611614i	0.0530380	+	0.0254398i
$579$	−1.10656	+	1.10656i	−0.0459872	+	0.0459872i
$580$	0.373712	+	0.465629i	0.0155175	+	0.0193342i
$581$	−6.92561	−	6.92561i	−0.287323	−	0.287323i
$582$	1.50493	−	0.529237i	0.0623814	−	0.0219376i
$583$		−	23.5554i		−	0.975566i
$584$	−9.20568	+	2.14655i	−0.380934	+	0.0888251i
$585$		−	0.853868i		−	0.0353031i
$586$	−8.50119	−	24.1739i	−0.351181	−	0.998613i
$587$	−22.4089	−	22.4089i	−0.924913	−	0.924913i	0.0724581	−	0.997371i	$-0.476916\pi$
$587$	−22.4089	−	22.4089i	−0.924913	−	0.924913i	−0.997371	+	0.0724581i	$0.976916\pi$
$588$	1.85929	+	0.203613i	0.0766758	+	0.00839687i
$589$	−33.0084	+	33.0084i	−1.36009	+	1.36009i
$590$	0.111473	−	0.232404i	0.00458929	−	0.00956794i
$591$	−3.48127			−0.143200
$592$	−28.2301	+	17.9850i	−1.16025	+	0.739180i
$593$	11.7801			0.483752			0.241876	−	0.970307i	$-0.422237\pi$
$593$	11.7801			0.483752			0.241876	+	0.970307i	$0.422237\pi$
$594$	2.32429	−	4.84578i	0.0953668	−	0.198825i
$595$	−0.0555881	+	0.0555881i	−0.00227889	+	0.00227889i
$596$	1.82265	−	16.6435i	0.0746586	−	0.681743i
$597$	−1.98331	−	1.98331i	−0.0811716	−	0.0811716i
$598$	−4.07164	−	11.5780i	−0.166502	−	0.473462i
$599$		−	37.4799i		−	1.53139i	−0.643204	−	0.765695i	$-0.722395\pi$
$599$		−	37.4799i		−	1.53139i	0.643204	−	0.765695i	$-0.277605\pi$
$600$	1.56791	−	2.52145i	0.0640095	−	0.102938i
$601$		−	20.0084i		−	0.816160i	−0.912946	−	0.408080i	$-0.866198\pi$
$601$		−	20.0084i		−	0.816160i	0.912946	−	0.408080i	$-0.133802\pi$
$602$	25.0487	−	8.80883i	1.02091	−	0.359021i
$603$	10.3370	+	10.3370i	0.420957	+	0.420957i
$604$	−28.9231	+	23.2136i	−1.17687	+	0.944546i
$605$	−0.0617391	+	0.0617391i	−0.00251005	+	0.00251005i
$606$	1.73415	+	0.831791i	0.0704452	+	0.0337892i
$607$	23.5587			0.956219			0.478109	−	0.878300i	$-0.341322\pi$
$607$	23.5587			0.956219			0.478109	+	0.878300i	$0.341322\pi$
$608$	2.98167	+	24.7264i	0.120923	+	1.00279i
$609$	−2.03229			−0.0823527
$610$	−0.271842	−	0.130390i	−0.0110066	−	0.00527933i
$611$	−15.4026	+	15.4026i	−0.623124	+	0.623124i
$612$	4.61046	−	3.70033i	0.186367	−	0.149577i
$613$	20.1218	+	20.1218i	0.812710	+	0.812710i	0.985039	−	0.172329i	$-0.0551292\pi$
$613$	20.1218	+	20.1218i	0.812710	+	0.812710i	−0.172329	+	0.985039i	$0.555129\pi$
$614$	15.9063	−	5.59376i	0.641927	−	0.225746i
$615$			0.121058i			0.00488151i
$616$	11.6460	+	7.24181i	0.469232	+	0.291781i
$617$			30.5796i			1.23109i	0.788103	+	0.615544i	$0.211064\pi$
$617$			30.5796i			1.23109i	−0.788103	+	0.615544i	$0.788936\pi$
$618$	1.16627	+	3.31638i	0.0469141	+	0.133404i
$619$	−20.3964	−	20.3964i	−0.819801	−	0.819801i	0.166278	−	0.986079i	$-0.446825\pi$
$619$	−20.3964	−	20.3964i	−0.819801	−	0.819801i	−0.986079	+	0.166278i	$0.946825\pi$
$620$	−0.113693	+	1.03818i	−0.00456602	+	0.0416945i
$621$	1.30892	−	1.30892i	0.0525250	−	0.0525250i
$622$	−11.0132	+	22.9607i	−0.441588	+	0.920641i
$623$	−15.0822			−0.604254
$624$	4.81135	+	1.06659i	0.192608	+	0.0426977i
$625$	−24.9636			−0.998545
$626$	4.42189	−	9.21894i	0.176734	−	0.368463i
$627$	−1.98643	+	1.98643i	−0.0793302	+	0.0793302i
$628$	14.6895	+	1.60867i	0.586174	+	0.0641928i
$629$	−5.91713	−	5.91713i	−0.235931	−	0.235931i
$630$	0.109022	+	0.310012i	0.00434352	+	0.0123512i
$631$		−	17.1518i		−	0.682801i	−0.939918	−	0.341400i	$-0.889099\pi$
$631$		−	17.1518i		−	0.682801i	0.939918	−	0.341400i	$-0.110901\pi$
$632$	2.12600	+	9.11754i	0.0845679	+	0.362676i
$633$		−	3.54138i		−	0.140757i
$634$	12.2995	−	4.32534i	0.488475	−	0.171781i
$635$	0.0760299	+	0.0760299i	0.00301715	+	0.00301715i
$636$	2.03912	+	2.54066i	0.0808565	+	0.100744i
$637$	18.4650	−	18.4650i	0.731611	−	0.731611i
$638$	23.4777	+	11.2611i	0.929490	+	0.445832i
$639$	−9.63473			−0.381144
$640$	0.398289	+	0.389676i	0.0157438	+	0.0154033i
$641$	15.9028			0.628124			0.314062	−	0.949402i	$-0.398310\pi$
$641$	15.9028			0.628124			0.314062	+	0.949402i	$0.398310\pi$
$642$	−3.89178	−	1.86670i	−0.153596	−	0.0736729i
$643$	−19.4064	+	19.4064i	−0.765312	+	0.765312i	−0.977277	−	0.211965i	$-0.932014\pi$
$643$	−19.4064	+	19.4064i	−0.765312	+	0.765312i	0.211965	+	0.977277i	$0.432014\pi$
$644$	2.95656	+	3.68375i	0.116505	+	0.145160i
$645$	0.0860469	+	0.0860469i	0.00338809	+	0.00338809i
$646$	−5.87375	+	2.06561i	−0.231100	+	0.0812705i
$647$			30.4133i			1.19567i	0.801620	+	0.597834i	$0.203972\pi$
$647$			30.4133i			1.19567i	−0.801620	+	0.597834i	$0.796028\pi$
$648$	−5.52684	−	23.7023i	−0.217115	−	0.931115i
$649$		−	11.2413i		−	0.441259i
$650$	−13.7525	−	39.1063i	−0.539416	−	1.53387i
$651$	−2.51375	−	2.51375i	−0.0985216	−	0.0985216i
$652$	−2.61679	−	0.286568i	−0.102481	−	0.0112229i
$653$	24.8266	−	24.8266i	0.971540	−	0.971540i	−0.0280657	−	0.999606i	$-0.508935\pi$
$653$	24.8266	−	24.8266i	0.971540	−	0.971540i	0.999606	+	0.0280657i	$0.00893476\pi$
$654$	−0.459615	+	0.958226i	−0.0179724	+	0.0374696i
$655$	−0.495380			−0.0193561
$656$	45.6972	+	10.1302i	1.78417	+	0.395518i
$657$	−9.87857			−0.385400
$658$	3.62560	−	7.55881i	0.141341	−	0.294673i
$659$	4.37388	−	4.37388i	0.170382	−	0.170382i	−0.616765	−	0.787147i	$-0.711557\pi$
$659$	4.37388	−	4.37388i	0.170382	−	0.170382i	0.787147	+	0.616765i	$0.211557\pi$
$660$	−0.00684196	+	0.0624772i	−0.000266323	+	0.00243192i
$661$	1.83816	+	1.83816i	0.0714960	+	0.0714960i	0.741951	−	0.670455i	$-0.233901\pi$
$661$	1.83816	+	1.83816i	0.0714960	+	0.0714960i	−0.670455	+	0.741951i	$0.733901\pi$
$662$	−8.53948	−	24.2827i	−0.331896	−	0.943776i
$663$			1.23204i			0.0478484i
$664$	−14.7383	−	9.16467i	−0.571957	−	0.355658i
$665$		−	0.346112i		−	0.0134217i
$666$	−32.9995	+	11.6049i	−1.27871	+	0.449681i
$667$	6.34166	+	6.34166i	0.245550	+	0.245550i
$668$	−27.3787	+	21.9740i	−1.05931	+	0.850199i
$669$	2.16106	−	2.16106i	0.0835515	−	0.0835515i
$670$	−0.310591	−	0.148976i	−0.0119992	−	0.00575543i
$671$	−13.1489			−0.507606
$672$	−1.88303	+	0.227068i	−0.0726394	+	0.00875934i
$673$	−22.6625			−0.873575			−0.436788	−	0.899565i	$-0.643884\pi$
$673$	−22.6625			−0.873575			−0.436788	+	0.899565i	$0.643884\pi$
$674$	16.6453	+	7.98398i	0.641154	+	0.307531i
$675$	4.42102	−	4.42102i	0.170165	−	0.170165i
$676$	33.3820	−	26.7922i	1.28392	−	1.03047i
$677$	31.3748	+	31.3748i	1.20583	+	1.20583i	0.972365	+	0.233465i	$0.0750065\pi$
$677$	31.3748	+	31.3748i	1.20583	+	1.20583i	0.233465	+	0.972365i	$0.424993\pi$
$678$	−3.67916	+	1.29385i	−0.141297	+	0.0496899i
$679$			8.57182i			0.328956i
$680$	−0.0735599	+	0.118296i	−0.00282089	+	0.00453646i
$681$		−	4.06102i		−	0.155619i
$682$	15.1107	+	42.9685i	0.578618	+	1.64535i
$683$	7.47978	+	7.47978i	0.286206	+	0.286206i	0.835578	−	0.549372i	$-0.185133\pi$
$683$	7.47978	+	7.47978i	0.286206	+	0.286206i	−0.549372	+	0.835578i	$0.685133\pi$
$684$	−2.83339	+	25.8731i	−0.108338	+	0.989281i
$685$	0.373608	−	0.373608i	0.0142748	−	0.0142748i
$686$	−11.1802	+	23.3090i	−0.426862	+	0.889941i
$687$	1.57637			0.0601422
$688$	39.6817	−	25.2807i	1.51285	−	0.963819i
$689$	45.4829			1.73276
$690$	−0.00936205	+	0.0195184i	−0.000356407	+	0.000743053i
$691$	10.3467	−	10.3467i	0.393606	−	0.393606i	−0.482365	−	0.875970i	$-0.660222\pi$
$691$	10.3467	−	10.3467i	0.393606	−	0.393606i	0.875970	+	0.482365i	$0.160222\pi$
$692$	−27.1286	−	2.97089i	−1.03127	−	0.112936i
$693$	10.1342	+	10.1342i	0.384967	+	0.384967i
$694$	−3.53359	−	10.0481i	−0.134133	−	0.381419i
$695$		−	1.14225i		−	0.0433279i
$696$	−3.50712	+	0.817780i	−0.132937	+	0.0309979i
$697$			11.7016i			0.443231i
$698$	19.0216	−	6.68929i	0.719977	−	0.253193i
$699$	2.44187	+	2.44187i	0.0923602	+	0.0923602i
$700$	9.98615	+	12.4423i	0.377441	+	0.470276i
$701$	6.46959	−	6.46959i	0.244353	−	0.244353i	−0.574295	−	0.818648i	$-0.694724\pi$
$701$	6.46959	−	6.46959i	0.244353	−	0.244353i	0.818648	+	0.574295i	$0.194724\pi$
$702$	9.35666	+	4.48794i	0.353144	+	0.169387i
$703$	36.8423			1.38953
$704$	23.0115	+	7.81087i	0.867280	+	0.294383i
$705$	0.0384206			0.00144700
$706$	−11.6573	−	5.59145i	−0.438728	−	0.210437i
$707$	−7.30758	+	7.30758i	−0.274830	+	0.274830i
$708$	0.973124	+	1.21247i	0.0365722	+	0.0455675i
$709$	−26.4374	−	26.4374i	−0.992876	−	0.992876i	0.00709906	−	0.999975i	$-0.497740\pi$
$709$	−26.4374	−	26.4374i	−0.992876	−	0.992876i	−0.999975	+	0.00709906i	$0.997740\pi$
$710$	0.214171	−	0.0753174i	0.00803771	−	0.00282661i
$711$			9.78399i			0.366928i
$712$	−26.0272	+	6.06896i	−0.975411	+	0.227444i
$713$			15.6880i			0.587521i
$714$	−0.157306	−	0.447314i	−0.00588704	−	0.0167403i
$715$	0.620475	+	0.620475i	0.0232044	+	0.0232044i
$716$	−12.1639	−	1.33208i	−0.454586	−	0.0497823i
$717$	−2.36462	+	2.36462i	−0.0883082	+	0.0883082i
$718$	−8.91450	+	18.5853i	−0.332686	+	0.693598i
$719$	32.5237			1.21293			0.606464	−	0.795111i	$-0.292587\pi$
$719$	32.5237			1.21293			0.606464	+	0.795111i	$0.292587\pi$
$720$	0.312885	+	0.491117i	0.0116605	+	0.0183028i
$721$	−18.8895			−0.703481
$722$	0.234768	−	0.489455i	0.00873718	−	0.0182156i
$723$	−0.666414	+	0.666414i	−0.0247842	+	0.0247842i
$724$	0.452979	−	4.13636i	0.0168348	−	0.153727i
$725$	21.4197	+	21.4197i	0.795509	+	0.795509i
$726$	−0.174713	−	0.496810i	−0.00648420	−	0.0184384i
$727$		−	26.8888i		−	0.997250i	−0.866818	−	0.498625i	$-0.833839\pi$
$727$		−	26.8888i		−	0.997250i	0.866818	−	0.498625i	$-0.166161\pi$
$728$	−13.9831	+	22.4872i	−0.518249	+	0.833430i
$729$		−	24.6465i		−	0.912832i
$730$	0.219592	−	0.0772235i	0.00812745	−	0.00285817i
$731$	8.31744	+	8.31744i	0.307632	+	0.307632i
$732$	1.41822	−	1.13826i	0.0524190	−	0.0420713i
$733$	−26.0476	+	26.0476i	−0.962090	+	0.962090i	−0.999307	−	0.0372169i	$-0.988151\pi$
$733$	−26.0476	+	26.0476i	−0.962090	+	0.962090i	0.0372169	+	0.999307i	$0.488151\pi$
$734$	5.38832	+	2.58452i	0.198887	+	0.0953965i
$735$	−0.0460594			−0.00169893
$736$	6.58444	+	5.16733i	0.242706	+	0.190470i
$737$	−15.0231			−0.553383
$738$	44.1046	+	21.1549i	1.62351	+	0.778721i
$739$	29.7745	−	29.7745i	1.09527	−	1.09527i	0.100316	−	0.994956i	$-0.468015\pi$
$739$	29.7745	−	29.7745i	1.09527	−	1.09527i	0.994956	−	0.100316i	$-0.0319853\pi$
$740$	0.642831	−	0.515933i	0.0236310	−	0.0189661i
$741$	−3.83557	−	3.83557i	−0.140903	−	0.140903i
$742$	−16.5134	+	5.80724i	−0.606225	+	0.213190i
$743$		−	45.6957i		−	1.67641i	−0.545352	−	0.838207i	$-0.683604\pi$
$743$		−	45.6957i		−	1.67641i	0.545352	−	0.838207i	$-0.316396\pi$
$744$	−5.34948	−	3.32645i	−0.196121	−	0.121954i
$745$			0.412302i			0.0151056i
$746$	−6.16988	−	17.5446i	−0.225895	−	0.642352i
$747$	−12.8251	−	12.8251i	−0.469245	−	0.469245i
$748$	−0.661356	+	6.03915i	−0.0241816	+	0.220813i
$749$	16.3996	−	16.3996i	0.599230	−	0.599230i
$750$	−0.0632583	+	0.131884i	−0.00230987	+	0.00481571i
$751$	−14.1028			−0.514619			−0.257309	−	0.966329i	$-0.582836\pi$
$751$	−14.1028			−0.514619			−0.257309	+	0.966329i	$0.582836\pi$
$752$	3.21507	−	14.5031i	0.117242	−	0.528874i
$753$	−1.82084			−0.0663551
$754$	−21.7440	+	45.3328i	−0.791869	+	1.65092i
$755$	0.645780	−	0.645780i	0.0235024	−	0.0235024i
$756$	−3.97012	−	0.434774i	−0.144392	−	0.0158126i
$757$	17.1067	+	17.1067i	0.621752	+	0.621752i	0.945979	−	0.324227i	$-0.105104\pi$
$757$	17.1067	+	17.1067i	0.621752	+	0.621752i	−0.324227	+	0.945979i	$0.605104\pi$
$758$	16.5453	+	47.0478i	0.600951	+	1.70885i
$759$			0.944094i			0.0342685i
$760$	−0.139273	−	0.597284i	−0.00505197	−	0.0216658i
$761$		−	26.0666i		−	0.944915i	−0.881353	−	0.472457i	$-0.843367\pi$
$761$		−	26.0666i		−	0.944915i	0.881353	−	0.472457i	$-0.156633\pi$
$762$	−0.611807	+	0.215154i	−0.0221634	+	0.00779419i
$763$	−4.03788	−	4.03788i	−0.146181	−	0.146181i
$764$	24.4330	+	30.4425i	0.883955	+	1.10137i
$765$	−0.102940	+	0.102940i	−0.00372180	+	0.00372180i
$766$	−19.6230	−	9.41222i	−0.709008	−	0.340077i
$767$	21.7056			0.783745
$768$	−3.15816	+	1.14957i	−0.113960	+	0.0414814i
$769$	23.9669			0.864267			0.432133	−	0.901810i	$-0.357761\pi$
$769$	23.9669			0.864267			0.432133	+	0.901810i	$0.357761\pi$
$770$	−0.304497	−	0.146053i	−0.0109733	−	0.00526337i
$771$	−3.84675	+	3.84675i	−0.138537	+	0.138537i
$772$	−9.32638	−	11.6203i	−0.335664	−	0.418223i
$773$	−10.3713	−	10.3713i	−0.373028	−	0.373028i	0.495551	−	0.868579i	$-0.334966\pi$
$773$	−10.3713	−	10.3713i	−0.373028	−	0.373028i	−0.868579	+	0.495551i	$0.834966\pi$
$774$	46.3860	−	16.3125i	1.66731	−	0.586340i
$775$			52.9882i			1.90339i
$776$	3.44924	+	14.7923i	0.123820	+	0.531014i
$777$			2.80571i			0.100654i
$778$	10.4495	+	29.7142i	0.374634	+	1.06530i
$779$	−36.4294	−	36.4294i	−1.30522	−	1.30522i
$780$	−0.120636	−	0.0132111i	−0.00431948	−	0.000473032i
$781$	7.00121	−	7.00121i	0.250523	−	0.250523i
$782$	−0.904952	+	1.88668i	−0.0323610	+	0.0674676i
$783$	−7.58312			−0.270999
$784$	−3.85429	+	17.3866i	−0.137653	+	0.620951i
$785$	−0.363897			−0.0129880
$786$	1.29222	−	2.69407i	0.0460919	−	0.0960943i
$787$	−12.3830	+	12.3830i	−0.441407	+	0.441407i	−0.892485	−	0.451077i	$-0.851040\pi$
$787$	−12.3830	+	12.3830i	−0.441407	+	0.441407i	0.451077	+	0.892485i	$0.351040\pi$
$788$	3.60833	−	32.9494i	0.128541	−	1.17377i
$789$	−1.39986	−	1.39986i	−0.0498364	−	0.0498364i
$790$	−0.0764842	−	0.217489i	−0.00272118	−	0.00773792i
$791$		−	20.9558i		−	0.745104i
$792$	21.5665	+	13.4106i	0.766332	+	0.476526i
$793$		−	25.3890i		−	0.901590i
$794$	−21.3632	+	7.51277i	−0.758152	+	0.266618i
$795$	−0.0567266	−	0.0567266i	−0.00201188	−	0.00201188i
$796$	20.8272	−	16.7159i	0.738202	−	0.592478i
$797$	8.15568	−	8.15568i	0.288889	−	0.288889i	−0.547752	−	0.836641i	$-0.684516\pi$
$797$	8.15568	−	8.15568i	0.288889	−	0.288889i	0.836641	+	0.547752i	$0.184516\pi$
$798$	1.88229	+	0.902847i	0.0666325	+	0.0319604i
$799$	3.71380			0.131385
$800$	22.2397	+	17.4533i	0.786294	+	0.617067i
$801$	−27.9297			−0.986847
$802$	13.8904	+	6.66255i	0.490486	+	0.235263i
$803$	7.17839	−	7.17839i	0.253320	−	0.253320i
$804$	1.62038	−	1.30051i	0.0571463	−	0.0458653i
$805$	−0.0822489	−	0.0822489i	−0.00289889	−	0.00289889i
$806$	−82.9674	+	29.1770i	−2.92240	+	1.02772i
$807$		−	1.59189i		−	0.0560373i
$808$	−9.67013	+	15.5512i	−0.340194	+	0.547088i
$809$			22.7960i			0.801464i	0.916195	+	0.400732i	$0.131244\pi$
$809$			22.7960i			0.801464i	−0.916195	+	0.400732i	$0.868756\pi$
$810$	0.198831	+	0.565394i	0.00698622	+	0.0198659i
$811$	−31.1481	−	31.1481i	−1.09376	−	1.09376i	−0.995124	−	0.0986356i	$-0.968552\pi$
$811$	−31.1481	−	31.1481i	−1.09376	−	1.09376i	−0.0986356	−	0.995124i	$-0.531448\pi$
$812$	2.10647	−	19.2351i	0.0739225	−	0.675021i
$813$	−2.58840	+	2.58840i	−0.0907792	+	0.0907792i
$814$	15.5467	−	32.4124i	0.544912	−	1.13606i
$815$	0.0648247			0.00227071
$816$	−0.451458	−	0.708628i	−0.0158042	−	0.0248069i
$817$	−51.7875			−1.81181
$818$	2.71274	−	5.65563i	0.0948486	−	0.197744i
$819$	−19.5680	+	19.5680i	−0.683763	+	0.683763i
$820$	−1.14578	−	0.125476i	−0.0400123	−	0.00438181i
$821$	−4.62263	−	4.62263i	−0.161331	−	0.161331i	0.621825	−	0.783156i	$-0.286391\pi$
$821$	−4.62263	−	4.62263i	−0.161331	−	0.161331i	−0.783156	+	0.621825i	$0.786391\pi$
$822$	1.05726	+	3.00640i	0.0368761	+	0.104860i
$823$			39.4325i			1.37453i	0.726406	+	0.687265i	$0.241189\pi$
$823$			39.4325i			1.37453i	−0.726406	+	0.687265i	$0.758811\pi$
$824$	−32.5975	+	7.60099i	−1.13559	+	0.264793i
$825$			3.18879i			0.111020i
$826$	−7.88062	+	2.77137i	−0.274202	+	0.0964283i
$827$	22.6279	+	22.6279i	0.786848	+	0.786848i	0.980976	−	0.194128i	$-0.0621878\pi$
$827$	22.6279	+	22.6279i	0.786848	+	0.786848i	−0.194128	+	0.980976i	$0.562188\pi$
$828$	5.47506	+	6.82170i	0.190272	+	0.237070i
$829$	−24.1572	+	24.1572i	−0.839013	+	0.839013i	−0.988729	−	0.149716i	$-0.952164\pi$
$829$	−24.1572	+	24.1572i	−0.839013	+	0.839013i	0.149716	+	0.988729i	$0.452164\pi$
$830$	0.385347	+	0.184833i	0.0133756	+	0.00641564i
$831$	−5.55683			−0.192764
$832$	−15.0819	+	44.4327i	−0.522872	+	1.54043i
$833$	−4.45218			−0.154259
$834$	6.21199	+	2.97960i	0.215104	+	0.103175i
$835$	0.611297	−	0.611297i	0.0211548	−	0.0211548i
$836$	−16.7421	−	20.8599i	−0.579037	−	0.721456i
$837$	−9.37958	−	9.37958i	−0.324206	−	0.324206i
$838$	17.2531	−	6.06736i	0.595997	−	0.209594i
$839$			10.8781i			0.375555i	0.982212	+	0.187777i	$0.0601284\pi$
$839$			10.8781i			0.375555i	−0.982212	+	0.187777i	$0.939872\pi$
$840$	0.0454860	−	0.0106063i	0.00156942	−	0.000365952i
$841$		−	7.74001i		−	0.266897i
$842$	−0.709009	−	2.01613i	−0.0244341	−	0.0694803i
$843$	−0.728210	−	0.728210i	−0.0250809	−	0.0250809i
$844$	33.5183	+	3.67063i	1.15375	+	0.126348i
$845$	−0.745336	+	0.745336i	−0.0256403	+	0.0256403i
$846$	6.71401	−	13.9977i	0.230832	−	0.481249i
$847$	2.82974			0.0972311
$848$	−26.1602	+	16.6664i	−0.898347	+	0.572326i
$849$	2.80001			0.0960962
$850$	−3.05659	+	6.37250i	−0.104840	+	0.218575i
$851$	8.75506	−	8.75506i	0.300120	−	0.300120i
$852$	−0.149069	+	1.36122i	−0.00510701	+	0.0466345i
$853$	−30.7588	−	30.7588i	−1.05316	−	1.05316i	−0.998505	−	0.0546567i	$-0.982594\pi$
$853$	−30.7588	−	30.7588i	−1.05316	−	1.05316i	−0.0546567	−	0.998505i	$-0.517406\pi$
$854$	3.24166	+	9.21793i	0.110927	+	0.315431i
$855$		−	0.640943i		−	0.0219198i
$856$	21.7017	−	34.8999i	0.741748	−	1.19285i
$857$			13.0611i			0.446159i	0.974800	+	0.223079i	$0.0716109\pi$
$857$			13.0611i			0.446159i	−0.974800	+	0.223079i	$0.928389\pi$
$858$	−4.99292	+	1.75585i	−0.170455	+	0.0599439i
$859$	10.8913	+	10.8913i	0.371605	+	0.371605i	0.868061	−	0.496457i	$-0.165366\pi$
$859$	10.8913	+	10.8913i	0.371605	+	0.371605i	−0.496457	+	0.868061i	$0.665366\pi$
$860$	−0.903599	+	0.725224i	−0.0308125	+	0.0247299i
$861$	2.77427	−	2.77427i	0.0945468	−	0.0945468i
$862$	39.4632	+	18.9286i	1.34412	+	0.644712i
$863$	−23.0409			−0.784322			−0.392161	−	0.919897i	$-0.628272\pi$
$863$	−23.0409			−0.784322			−0.392161	+	0.919897i	$0.628272\pi$
$864$	−7.02617	+	0.847262i	−0.239035	+	0.0288244i
$865$	0.672045			0.0228502
$866$	8.31243	+	3.98708i	0.282468	+	0.135486i
$867$	0.148531	−	0.148531i	0.00504438	−	0.00504438i
$868$	26.3975	−	21.1865i	0.895989	−	0.719116i
$869$	−7.10967	−	7.10967i	−0.241179	−	0.241179i
$870$	0.0836586	−	0.0294201i	0.00283629	−	0.000997435i
$871$		−	29.0079i		−	0.982897i
$872$	−8.59297	−	5.34334i	−0.290995	−	0.180948i
$873$			15.8736i			0.537240i
$874$	−3.05631	−	8.69088i	−0.103381	−	0.293973i
$875$	−0.555746	−	0.555746i	−0.0187877	−	0.0187877i
$876$	−0.152841	+	1.39567i	−0.00516403	+	0.0471552i
$877$	9.22313	−	9.22313i	0.311443	−	0.311443i	−0.534025	−	0.845468i	$-0.679321\pi$
$877$	9.22313	−	9.22313i	0.311443	−	0.311443i	0.845468	+	0.534025i	$0.179321\pi$
$878$	11.9120	−	24.8346i	0.402010	−	0.838129i
$879$	−3.80613			−0.128377
$880$	−0.584239	−	0.129515i	−0.0196947	−	0.00436594i
$881$	25.2804			0.851718			0.425859	−	0.904789i	$-0.359972\pi$
$881$	25.2804			0.851718			0.425859	+	0.904789i	$0.359972\pi$
$882$	−8.04890	+	16.7807i	−0.271021	+	0.565035i
$883$	31.6766	−	31.6766i	1.06600	−	1.06600i	0.0683388	−	0.997662i	$-0.478230\pi$
$883$	31.6766	−	31.6766i	1.06600	−	1.06600i	0.997662	−	0.0683388i	$-0.0217699\pi$
$884$	−11.6609	−	1.27700i	−0.392199	−	0.0429503i
$885$	−0.0270714	−	0.0270714i	−0.000909996	−	0.000909996i
$886$	−4.30756	−	12.2489i	−0.144715	−	0.411510i
$887$		−	11.1503i		−	0.374390i	−0.982323	−	0.187195i	$-0.940060\pi$
$887$		−	11.1503i		−	0.374390i	0.982323	−	0.187195i	$-0.0599396\pi$
$888$	1.12900	+	4.84180i	0.0378867	+	0.162480i
$889$		−	3.48474i		−	0.116875i
$890$	0.620852	−	0.218334i	0.0208110	−	0.00731858i
$891$	18.4826	+	18.4826i	0.619190	+	0.619190i
$892$	18.2140	+	22.6938i	0.609848	+	0.759845i
$893$	−11.5617	+	11.5617i	−0.386899	+	0.386899i
$894$	−2.24226	−	1.07551i	−0.0749924	−	0.0359703i
$895$	0.301331			0.0100724
$896$	−0.197387	−	18.0577i	−0.00659423	−	0.603267i
$897$	−1.82294			−0.0608662
$898$	−4.86804	−	2.33497i	−0.162449	−	0.0779189i
$899$	45.4438	−	45.4438i	1.51564	−	1.51564i
$900$	18.4927	+	23.0411i	0.616423	+	0.768038i
$901$	−5.48329	−	5.48329i	−0.182675	−	0.182675i
$902$	−47.4216	+	16.6767i	−1.57897	+	0.555274i
$903$		−	3.94386i		−	0.131243i
$904$	−8.43248	−	36.1634i	−0.280460	−	1.20278i
$905$			0.102468i			0.00340617i
$906$	1.82746	+	5.19655i	0.0607134	+	0.172644i
$907$	9.48399	+	9.48399i	0.314911	+	0.314911i	0.846809	−	0.531898i	$-0.178521\pi$
$907$	9.48399	+	9.48399i	0.314911	+	0.314911i	−0.531898	+	0.846809i	$0.678521\pi$
$908$	38.4365	+	4.20924i	1.27556	+	0.139688i
$909$	−13.5324	+	13.5324i	−0.448842	+	0.448842i
$910$	0.282011	−	0.587949i	0.00934857	−	0.0194903i
$911$	49.8313			1.65098			0.825492	−	0.564414i	$-0.190898\pi$
$911$	49.8313			1.65098			0.825492	+	0.564414i	$0.190898\pi$
$912$	3.61156	+	0.800617i	0.119591	+	0.0265111i
$913$	18.6390			0.616862
$914$	−20.4605	+	42.6568i	−0.676772	+	1.41096i
$915$	−0.0316653	+	0.0316653i	−0.00104682	+	0.00104682i
$916$	−1.63390	+	14.9199i	−0.0539856	+	0.492968i
$917$	11.3526	+	11.3526i	0.374896	+	0.374896i
$918$	−0.586959	−	1.66907i	−0.0193725	−	0.0550874i
$919$			27.3756i			0.903036i	0.892262	+	0.451518i	$0.149117\pi$
$919$			27.3756i			0.903036i	−0.892262	+	0.451518i	$0.850883\pi$
$920$	−0.175033	−	0.108840i	−0.00577066	−	0.00358835i
$921$		−	2.50442i		−	0.0825234i
$922$	14.2109	−	4.99752i	0.468011	−	0.164585i
$923$	13.5186	+	13.5186i	0.444969	+	0.444969i
$924$	1.58858	−	1.27499i	0.0522605	−	0.0419440i
$925$	29.5713	−	29.5713i	0.972298	−	0.972298i
$926$	−41.8790	−	20.0874i	−1.37623	−	0.660112i
$927$	−34.9802			−1.14890
$928$	−4.10496	−	34.0416i	−0.134752	−	1.11747i
$929$	−47.2229			−1.54933			−0.774667	−	0.632370i	$-0.782082\pi$
$929$	−47.2229			−1.54933			−0.774667	+	0.632370i	$0.782082\pi$
$930$	0.139867	+	0.0670877i	0.00458643	+	0.00219989i
$931$	13.8605	−	13.8605i	0.454259	−	0.454259i
$932$	−25.6427	+	20.5807i	−0.839955	+	0.674144i
$933$	2.67456	+	2.67456i	0.0875612	+	0.0875612i
$934$	−10.3141	+	3.62714i	−0.337487	+	0.118684i
$935$		−	0.149605i		−	0.00489262i
$936$	−25.8944	+	41.6425i	−0.846386	+	1.36113i
$937$		−	31.7949i		−	1.03870i	−0.854563	−	0.519348i	$-0.826175\pi$
$937$		−	31.7949i		−	1.03870i	0.854563	−	0.519348i	$-0.173825\pi$
$938$	3.70372	+	10.5319i	0.120931	+	0.343877i
$939$	−1.07386	−	1.07386i	−0.0350441	−	0.0350441i
$940$	−0.0398228	+	0.363641i	−0.00129888	+	0.0118607i
$941$	11.4894	−	11.4894i	0.374543	−	0.374543i	−0.494586	−	0.869129i	$-0.664680\pi$
$941$	11.4894	−	11.4894i	0.374543	−	0.374543i	0.869129	+	0.494586i	$0.164680\pi$
$942$	0.949239	−	1.97901i	0.0309279	−	0.0644797i
$943$	−17.3139			−0.563818
$944$	−12.4844	+	7.95364i	−0.406332	+	0.258869i
$945$	0.0983502			0.00319933
$946$	−21.8533	+	45.5607i	−0.710512	+	1.48131i
$947$	−37.6171	+	37.6171i	−1.22239	+	1.22239i	−0.255610	+	0.966780i	$0.582276\pi$
$947$	−37.6171	+	37.6171i	−1.22239	+	1.22239i	−0.966780	+	0.255610i	$0.917724\pi$
$948$	1.38230	+	0.151378i	0.0448951	+	0.00491653i
$949$	13.8607	+	13.8607i	0.449937	+	0.449937i
$950$	−10.3231	−	29.3545i	−0.334924	−	0.952386i
$951$		−	1.93653i		−	0.0627962i
$952$	4.39676	−	1.02522i	0.142500	−	0.0332277i
$953$		−	49.2058i		−	1.59393i	−0.604024	−	0.796966i	$-0.706437\pi$
$953$		−	49.2058i		−	1.59393i	0.604024	−	0.796966i	$-0.293563\pi$
$954$	−30.5800	+	10.7540i	−0.990065	+	0.348175i
$955$	−0.679704	−	0.679704i	−0.0219947	−	0.0219947i
$956$	−19.9296	−	24.8314i	−0.644568	−	0.803105i
$957$	2.73478	−	2.73478i	0.0884028	−	0.0884028i
$958$	52.6783	+	25.2673i	1.70196	+	0.816348i
$959$	−17.1239			−0.552960
$960$	0.0742270	−	0.0366065i	0.00239567	−	0.00118147i
$961$	81.4191			2.62642
$962$	62.5848	+	30.0189i	2.01781	+	0.967849i
$963$	30.3694	−	30.3694i	0.978641	−	0.978641i
$964$	−5.61670	−	6.99818i	−0.180902	−	0.225396i
$965$	0.259451	+	0.259451i	0.00835204	+	0.00835204i
$966$	0.661851	−	0.232752i	0.0212947	−	0.00748869i
$967$			29.0373i			0.933778i	0.884316	+	0.466889i	$0.154625\pi$
$967$			29.0373i			0.933778i	−0.884316	+	0.466889i	$0.845375\pi$
$968$	4.88327	−	1.13867i	0.156954	−	0.0365982i
$969$			0.924810i			0.0297092i
$970$	−0.124088	−	0.352856i	−0.00398423	−	0.0113295i
$971$	30.0244	+	30.0244i	0.963529	+	0.963529i	0.999358	−	0.0358287i	$-0.0114071\pi$
$971$	30.0244	+	30.0244i	0.963529	+	0.963529i	−0.0358287	+	0.999358i	$0.511407\pi$
$972$	−11.0552	−	1.21068i	−0.354597	−	0.0388324i
$973$	−26.1768	+	26.1768i	−0.839190	+	0.839190i
$974$	−18.2393	+	38.0261i	−0.584426	+	1.21844i
$975$	−6.15721			−0.197188
$976$	9.30334	+	14.6029i	0.297793	+	0.467428i
$977$	−20.8445			−0.666875			−0.333437	−	0.942772i	$-0.608209\pi$
$977$	−20.8445			−0.666875			−0.333437	+	0.942772i	$0.608209\pi$
$978$	−0.169098	+	0.352542i	−0.00540715	+	0.0112730i
$979$	20.2955	−	20.2955i	0.648646	−	0.648646i
$980$	0.0477404	−	0.435940i	0.00152501	−	0.0139256i
$981$	−7.47749	−	7.47749i	−0.238738	−	0.238738i
$982$	−1.75989	−	5.00440i	−0.0561604	−	0.159697i
$983$			13.1767i			0.420273i	0.977672	+	0.210136i	$0.0673908\pi$
$983$			13.1767i			0.420273i	−0.977672	+	0.210136i	$0.932609\pi$
$984$	3.67119	−	5.90388i	0.117033	−	0.188209i
$985$			0.816241i			0.0260076i
$986$	8.08658	−	2.84380i	0.257529	−	0.0905650i
$987$	−0.880481	−	0.880481i	−0.0280260	−	0.0280260i
$988$	40.2782	−	32.3271i	1.28142	−	1.02846i
$989$	−12.3066	+	12.3066i	−0.391327	+	0.391327i
$990$	−0.563877	−	0.270465i	−0.0179212	−	0.00859594i
$991$	−16.3992			−0.520938			−0.260469	−	0.965482i	$-0.583877\pi$
$991$	−16.3992			−0.520938			−0.260469	+	0.965482i	$0.583877\pi$
$992$	37.0287	−	47.1836i	1.17566	−	1.49808i
$993$	−3.82327			−0.121328
$994$	−6.63420	−	3.18211i	−0.210424	−	0.100930i
$995$	−0.465020	+	0.465020i	−0.0147421	+	0.0147421i
$996$	−2.01039	+	1.61353i	−0.0637015	+	0.0511266i
$997$	−4.21796	−	4.21796i	−0.133584	−	0.133584i	0.637153	−	0.770737i	$-0.280112\pi$
$997$	−4.21796	−	4.21796i	−0.133584	−	0.133584i	−0.770737	+	0.637153i	$0.780112\pi$
$998$	−21.8264	+	7.67566i	−0.690902	+	0.242969i
$999$			10.4690i			0.331224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.b.69.14	✓	30
4.3	odd	2		1088.2.l.b.817.7		30
16.3	odd	4		1088.2.l.b.273.7		30
16.13	even	4	inner	272.2.l.b.205.14	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.14	✓	30	1.1	even	1	trivial
272.2.l.b.205.14	yes	30	16.13	even	4	inner
1088.2.l.b.273.7		30	16.3	odd	4
1088.2.l.b.817.7		30	4.3	odd	2

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27512 + 0.611614i) q^{2} +(0.148531 - 0.148531i) q^{3} +(1.25186 + 1.55976i) q^{4} +(-0.0348255 - 0.0348255i) q^{5} +(0.280239 - 0.0985512i) q^{6} +1.59619i q^{7} +(0.642295 + 2.75453i) q^{8} +2.95588i q^{9} +(-0.0231069 - 0.0657065i) q^{10} +(-2.14793 - 2.14793i) q^{11} +(0.417613 + 0.0457334i) q^{12} +(4.14741 - 4.14741i) q^{13} +(-0.976251 + 2.03533i) q^{14} -0.0103454 q^{15} +(-0.865709 + 3.90519i) q^{16} -1.00000 q^{17} +(-1.80786 + 3.76909i) q^{18} +(3.11319 - 3.11319i) q^{19} +(0.0107229 - 0.0979161i) q^{20} +(0.237084 + 0.237084i) q^{21} +(-1.42516 - 4.05257i) q^{22} -1.47961i q^{23} +(0.504535 + 0.313733i) q^{24} -4.99757i q^{25} +(7.82505 - 2.75183i) q^{26} +(0.884633 + 0.884633i) q^{27} +(-2.48967 + 1.99820i) q^{28} +(-4.28602 + 4.28602i) q^{29} +(-0.0131916 - 0.00632736i) q^{30} -10.6028 q^{31} +(-3.49235 + 4.45011i) q^{32} -0.638069 q^{33} +(-1.27512 - 0.611614i) q^{34} +(0.0555881 - 0.0555881i) q^{35} +(-4.61046 + 3.70033i) q^{36} +(5.91713 + 5.91713i) q^{37} +(5.87375 - 2.06561i) q^{38} -1.23204i q^{39} +(0.0735599 - 0.118296i) q^{40} -11.7016i q^{41} +(0.157306 + 0.447314i) q^{42} +(-8.31744 - 8.31744i) q^{43} +(0.661356 - 6.03915i) q^{44} +(0.102940 - 0.102940i) q^{45} +(0.904952 - 1.88668i) q^{46} -3.71380 q^{47} +(0.451458 + 0.708628i) q^{48} +4.45218 q^{49} +(3.05659 - 6.37250i) q^{50} +(-0.148531 + 0.148531i) q^{51} +(11.6609 + 1.27700i) q^{52} +(5.48329 + 5.48329i) q^{53} +(0.586959 + 1.66907i) q^{54} +0.149605i q^{55} +(-4.39676 + 1.02522i) q^{56} -0.924810i q^{57} +(-8.08658 + 2.84380i) q^{58} +(2.61677 + 2.61677i) q^{59} +(-0.0129509 - 0.0161363i) q^{60} +(3.06083 - 3.06083i) q^{61} +(-13.5198 - 6.48481i) q^{62} -4.71814 q^{63} +(-7.17491 + 3.53845i) q^{64} -0.288871 q^{65} +(-0.813613 - 0.390252i) q^{66} +(3.49712 - 3.49712i) q^{67} +(-1.25186 - 1.55976i) q^{68} +(-0.219769 - 0.219769i) q^{69} +(0.104880 - 0.0368830i) q^{70} +3.25952i q^{71} +(-8.14206 + 1.89854i) q^{72} +3.34201i q^{73} +(3.92605 + 11.1640i) q^{74} +(-0.742296 - 0.742296i) q^{75} +(8.75309 + 0.958563i) q^{76} +(3.42850 - 3.42850i) q^{77} +(0.753532 - 1.57100i) q^{78} +3.31001 q^{79} +(0.166149 - 0.105852i) q^{80} -8.60484 q^{81} +(7.15688 - 14.9210i) q^{82} +(-4.33884 + 4.33884i) q^{83} +(-0.0729991 + 0.666589i) q^{84} +(0.0348255 + 0.0348255i) q^{85} +(-5.51866 - 15.6928i) q^{86} +1.27322i q^{87} +(4.53694 - 7.29614i) q^{88} +9.44887i q^{89} +(0.194220 - 0.0683012i) q^{90} +(6.62005 + 6.62005i) q^{91} +(2.30784 - 1.85226i) q^{92} +(-1.57484 + 1.57484i) q^{93} +(-4.73554 - 2.27141i) q^{94} -0.216837 q^{95} +(0.142256 + 1.17970i) q^{96} +5.37018 q^{97} +(5.67706 + 2.72302i) q^{98} +(6.34901 - 6.34901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Introduction

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