LMFDB - Embedded newform 273.2.bf.b.185.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(152,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

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

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

chi := DirichletCharacter("273.152");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bf (of order $6$, degree $2$, 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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.9
Character	$\chi$	$=$	273.185
Dual form			273.2.bf.b.152.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33345 - 0.769868i) q^{2} +(-0.674223 - 1.59544i) q^{3} +(0.185393 + 0.321109i) q^{4} +(0.956175 + 1.65614i) q^{5} +(-0.329235 + 2.64650i) q^{6} +(1.55646 + 2.13949i) q^{7} +2.50856i q^{8} +(-2.09085 + 2.15136i) q^{9} -2.94451i q^{10} +2.30765i q^{11} +(0.387315 - 0.512282i) q^{12} +(0.963713 + 3.47437i) q^{13} +(-0.428341 - 4.05118i) q^{14} +(1.99760 - 2.64213i) q^{15} +(2.30204 - 3.98726i) q^{16} +(-1.87695 - 3.25097i) q^{17} +(4.44430 - 1.25906i) q^{18} +4.83490i q^{19} +(-0.354536 + 0.614074i) q^{20} +(2.36402 - 3.92573i) q^{21} +(1.77659 - 3.07714i) q^{22} +(0.175563 + 0.101362i) q^{23} +(4.00225 - 1.69133i) q^{24} +(0.671459 - 1.16300i) q^{25} +(1.38974 - 5.37483i) q^{26} +(4.84206 + 1.88532i) q^{27} +(-0.398454 + 0.896441i) q^{28} +(0.228216 - 0.131761i) q^{29} +(-4.69779 + 1.98526i) q^{30} +(1.76906 + 1.02137i) q^{31} +(-1.79437 + 1.03598i) q^{32} +(3.68172 - 1.55587i) q^{33} +5.78001i q^{34} +(-2.05505 + 4.62345i) q^{35} +(-1.07845 - 0.272545i) q^{36} +(-2.25673 + 3.90878i) q^{37} +(3.72223 - 6.44709i) q^{38} +(4.89339 - 3.88004i) q^{39} +(-4.15454 + 2.39862i) q^{40} +(-5.87191 - 10.1704i) q^{41} +(-6.17460 + 3.41479i) q^{42} +(-2.00837 + 3.47860i) q^{43} +(-0.741009 + 0.427822i) q^{44} +(-5.56218 - 1.40567i) q^{45} +(-0.156070 - 0.270321i) q^{46} +(4.81266 + 8.33577i) q^{47} +(-7.91351 - 0.984471i) q^{48} +(-2.15484 + 6.66008i) q^{49} +(-1.79071 + 1.03387i) q^{50} +(-3.92124 + 5.18643i) q^{51} +(-0.936988 + 0.953580i) q^{52} +(9.35130 + 5.39898i) q^{53} +(-5.00520 - 6.24173i) q^{54} +(-3.82180 + 2.20652i) q^{55} +(-5.36704 + 3.90448i) q^{56} +(7.71378 - 3.25980i) q^{57} -0.405753 q^{58} +(-1.95014 - 3.37774i) q^{59} +(1.21875 + 0.151617i) q^{60} -10.8438i q^{61} +(-1.57263 - 2.72388i) q^{62} +(-7.85715 - 1.12484i) q^{63} -6.01791 q^{64} +(-4.83258 + 4.91815i) q^{65} +(-6.10720 - 0.759759i) q^{66} +5.80716 q^{67} +(0.695945 - 1.20541i) q^{68} +(0.0433474 - 0.348441i) q^{69} +(6.29976 - 4.58303i) q^{70} +(1.76608 + 1.01965i) q^{71} +(-5.39682 - 5.24502i) q^{72} +(-4.51243 - 2.60525i) q^{73} +(6.01849 - 3.47477i) q^{74} +(-2.30821 - 0.287150i) q^{75} +(-1.55253 + 0.896354i) q^{76} +(-4.93720 + 3.59178i) q^{77} +(-9.51221 + 1.40658i) q^{78} +(2.21921 + 3.84378i) q^{79} +8.80463 q^{80} +(-0.256710 - 8.99634i) q^{81} +18.0824i q^{82} -4.19536 q^{83} +(1.69886 + 0.0313080i) q^{84} +(3.58938 - 6.21699i) q^{85} +(5.35612 - 3.09236i) q^{86} +(-0.364084 - 0.275269i) q^{87} -5.78888 q^{88} +(-5.94831 + 10.3028i) q^{89} +(6.33471 + 6.15653i) q^{90} +(-5.93340 + 7.46959i) q^{91} +0.0751668i q^{92} +(0.436788 - 3.51105i) q^{93} -14.8204i q^{94} +(-8.00728 + 4.62301i) q^{95} +(2.86265 + 2.16433i) q^{96} +(-0.681039 - 0.393198i) q^{97} +(8.00076 - 7.22194i) q^{98} +(-4.96459 - 4.82495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.33345	−	0.769868i	−0.942892	−	0.544379i	−0.0520260	−	0.998646i	$-0.516568\pi$
$2$	−1.33345	−	0.769868i	−0.942892	−	0.544379i	−0.890866	+	0.454267i	$0.849901\pi$
$3$	−0.674223	−	1.59544i	−0.389263	−	0.921127i
$3$	−0.674223	−	1.59544i	−0.389263	−	0.921127i
$4$	0.185393	+	0.321109i	0.0926963	+	0.160555i
$5$	0.956175	+	1.65614i	0.427614	+	0.740650i	0.996661	−	0.0816556i	$-0.0260208\pi$
$5$	0.956175	+	1.65614i	0.427614	+	0.740650i	−0.569046	+	0.822306i	$0.692687\pi$
$6$	−0.329235	+	2.64650i	−0.134409	+	1.08043i
$7$	1.55646	+	2.13949i	0.588288	+	0.808652i
$7$	1.55646	+	2.13949i	0.588288	+	0.808652i
$8$			2.50856i			0.886910i
$9$	−2.09085	+	2.15136i	−0.696949	+	0.717120i
$10$		−	2.94451i		−	0.931137i
$11$			2.30765i			0.695783i	0.937535	+	0.347892i	$0.113102\pi$
$11$			2.30765i			0.695783i	−0.937535	+	0.347892i	$0.886898\pi$
$12$	0.387315	−	0.512282i	0.111808	−	0.147883i
$13$	0.963713	+	3.47437i	0.267286	+	0.963617i
$13$	0.963713	+	3.47437i	0.267286	+	0.963617i
$14$	−0.428341	−	4.05118i	−0.114479	−	1.08272i
$15$	1.99760	−	2.64213i	0.515778	−	0.682194i
$16$	2.30204	−	3.98726i	0.575511	−	0.996814i
$17$	−1.87695	−	3.25097i	−0.455227	−	0.788476i	0.543474	−	0.839426i	$-0.317108\pi$
$17$	−1.87695	−	3.25097i	−0.455227	−	0.788476i	−0.998701	+	0.0509499i	$0.983775\pi$
$18$	4.44430	−	1.25906i	1.04753	−	0.296762i
$19$			4.83490i			1.10920i	0.832117	+	0.554601i	$0.187129\pi$
$19$			4.83490i			1.10920i	−0.832117	+	0.554601i	$0.812871\pi$
$20$	−0.354536	+	0.614074i	−0.0792766	+	0.137311i
$21$	2.36402	−	3.92573i	0.515872	−	0.856666i
$22$	1.77659	−	3.07714i	0.378770	−	0.656048i
$23$	0.175563	+	0.101362i	0.0366075	+	0.0211353i	0.518192	−	0.855264i	$-0.326605\pi$
$23$	0.175563	+	0.101362i	0.0366075	+	0.0211353i	−0.481585	+	0.876400i	$0.659939\pi$
$24$	4.00225	−	1.69133i	0.816956	−	0.345241i
$25$	0.671459	−	1.16300i	0.134292	−	0.232600i
$26$	1.38974	−	5.37483i	0.272551	−	1.05409i
$27$	4.84206	+	1.88532i	0.931855	+	0.362831i
$28$	−0.398454	+	0.896441i	−0.0753007	+	0.169411i
$29$	0.228216	−	0.131761i	0.0423786	−	0.0244673i	−0.478661	−	0.878000i	$-0.658878\pi$
$29$	0.228216	−	0.131761i	0.0423786	−	0.0244673i	0.521040	+	0.853532i	$0.325544\pi$
$30$	−4.69779	+	1.98526i	−0.857695	+	0.362457i
$31$	1.76906	+	1.02137i	0.317732	+	0.183443i	0.650381	−	0.759608i	$-0.274609\pi$
$31$	1.76906	+	1.02137i	0.317732	+	0.183443i	−0.332649	+	0.943051i	$0.607942\pi$
$32$	−1.79437	+	1.03598i	−0.317203	+	0.183137i
$33$	3.68172	−	1.55587i	0.640905	−	0.270842i
$34$			5.78001i			0.991263i
$35$	−2.05505	+	4.62345i	−0.347367	+	0.781507i
$36$	−1.07845	−	0.272545i	−0.179742	−	0.0454241i
$37$	−2.25673	+	3.90878i	−0.371005	+	0.642599i	−0.989720	−	0.143016i	$-0.954320\pi$
$37$	−2.25673	+	3.90878i	−0.371005	+	0.642599i	0.618715	+	0.785615i	$0.287653\pi$
$38$	3.72223	−	6.44709i	0.603826	−	1.04586i
$39$	4.89339	−	3.88004i	0.783569	−	0.621304i
$40$	−4.15454	+	2.39862i	−0.656890	+	0.379255i
$41$	−5.87191	−	10.1704i	−0.917038	−	1.58836i	−0.803889	−	0.594779i	$-0.797240\pi$
$41$	−5.87191	−	10.1704i	−0.917038	−	1.58836i	−0.113149	−	0.993578i	$-0.536094\pi$
$42$	−6.17460	+	3.41479i	−0.952762	+	0.526913i
$43$	−2.00837	+	3.47860i	−0.306273	+	0.530481i	−0.977544	−	0.210731i	$-0.932415\pi$
$43$	−2.00837	+	3.47860i	−0.306273	+	0.530481i	0.671271	+	0.741212i	$0.265749\pi$
$44$	−0.741009	+	0.427822i	−0.111711	+	0.0644966i
$45$	−5.56218	−	1.40567i	−0.829161	−	0.209544i
$46$	−0.156070	−	0.270321i	−0.0230113	−	0.0398567i
$47$	4.81266	+	8.33577i	0.701999	+	1.21590i	0.967764	+	0.251860i	$0.0810421\pi$
$47$	4.81266	+	8.33577i	0.701999	+	1.21590i	−0.265765	+	0.964038i	$0.585625\pi$
$48$	−7.91351	−	0.984471i	−1.14222	−	0.142096i
$49$	−2.15484	+	6.66008i	−0.307835	+	0.951440i
$50$	−1.79071	+	1.03387i	−0.253245	+	0.146211i
$51$	−3.92124	+	5.18643i	−0.549084	+	0.726246i
$52$	−0.936988	+	0.953580i	−0.129937	+	0.132238i
$53$	9.35130	+	5.39898i	1.28450	+	0.741606i	0.977668	−	0.210157i	$-0.0673976\pi$
$53$	9.35130	+	5.39898i	1.28450	+	0.741606i	0.306832	+	0.951764i	$0.400731\pi$
$54$	−5.00520	−	6.24173i	−0.681121	−	0.849392i
$55$	−3.82180	+	2.20652i	−0.515332	+	0.297527i
$56$	−5.36704	+	3.90448i	−0.717201	+	0.521758i
$57$	7.71378	−	3.25980i	1.02172	−	0.431771i
$58$	−0.405753			−0.0532779
$59$	−1.95014	−	3.37774i	−0.253886	−	0.439744i	0.710706	−	0.703489i	$-0.248376\pi$
$59$	−1.95014	−	3.37774i	−0.253886	−	0.439744i	−0.964592	+	0.263745i	$0.915042\pi$
$60$	1.21875	+	0.151617i	0.157340	+	0.0195737i
$61$		−	10.8438i		−	1.38841i	−0.719779	−	0.694203i	$-0.755757\pi$
$61$		−	10.8438i		−	1.38841i	0.719779	−	0.694203i	$-0.244243\pi$
$62$	−1.57263	−	2.72388i	−0.199725	−	0.345933i
$63$	−7.85715	−	1.12484i	−0.989907	−	0.141716i
$64$	−6.01791			−0.752238
$65$	−4.83258	+	4.91815i	−0.599408	+	0.610022i
$66$	−6.10720	−	0.759759i	−0.751744	−	0.0935199i
$67$	5.80716			0.709458			0.354729	−	0.934969i	$-0.384573\pi$
$67$	5.80716			0.709458			0.354729	+	0.934969i	$0.384573\pi$
$68$	0.695945	−	1.20541i	0.0843957	−	0.146178i
$69$	0.0433474	−	0.348441i	0.00521841	−	0.0419473i
$70$	6.29976	−	4.58303i	0.752965	−	0.547776i
$71$	1.76608	+	1.01965i	0.209595	+	0.121010i	0.601123	−	0.799156i	$-0.294720\pi$
$71$	1.76608	+	1.01965i	0.209595	+	0.121010i	−0.391528	+	0.920166i	$0.628053\pi$
$72$	−5.39682	−	5.24502i	−0.636021	−	0.618131i
$73$	−4.51243	−	2.60525i	−0.528140	−	0.304922i	0.212119	−	0.977244i	$-0.431964\pi$
$73$	−4.51243	−	2.60525i	−0.528140	−	0.304922i	−0.740259	+	0.672322i	$0.765297\pi$
$74$	6.01849	−	3.47477i	0.699635	−	0.403934i
$75$	−2.30821	−	0.287150i	−0.266529	−	0.0331572i
$76$	−1.55253	+	0.896354i	−0.178088	+	0.102819i
$77$	−4.93720	+	3.59178i	−0.562646	+	0.409321i
$78$	−9.51221	+	1.40658i	−1.07705	+	0.159264i
$79$	2.21921	+	3.84378i	0.249680	+	0.432459i	0.963437	−	0.267935i	$-0.0863412\pi$
$79$	2.21921	+	3.84378i	0.249680	+	0.432459i	−0.713757	+	0.700394i	$0.753008\pi$
$80$	8.80463			0.984387
$81$	−0.256710	−	8.99634i	−0.0285233	−	0.999593i
$82$			18.0824i			1.99686i
$83$	−4.19536			−0.460501			−0.230250	−	0.973131i	$-0.573955\pi$
$83$	−4.19536			−0.460501			−0.230250	+	0.973131i	$0.573955\pi$
$84$	1.69886	+	0.0313080i	0.185361	+	0.00341599i
$85$	3.58938	−	6.21699i	0.389323	−	0.674327i
$86$	5.35612	−	3.09236i	0.577565	−	0.333457i
$87$	−0.364084	−	0.275269i	−0.0390339	−	0.0295119i
$88$	−5.78888			−0.617097
$89$	−5.94831	+	10.3028i	−0.630520	+	1.09209i	0.356925	+	0.934133i	$0.383825\pi$
$89$	−5.94831	+	10.3028i	−0.630520	+	1.09209i	−0.987446	+	0.157960i	$0.949508\pi$
$90$	6.33471	+	6.15653i	0.667737	+	0.648955i
$91$	−5.93340	+	7.46959i	−0.621990	+	0.783025i
$92$			0.0751668i			0.00783668i
$93$	0.436788	−	3.51105i	0.0452928	−	0.364079i
$94$		−	14.8204i		−	1.52861i
$95$	−8.00728	+	4.62301i	−0.821530	+	0.474311i
$96$	2.86265	+	2.16433i	0.292168	+	0.220896i
$97$	−0.681039	−	0.393198i	−0.0691490	−	0.0399232i	0.465027	−	0.885297i	$-0.346045\pi$
$97$	−0.681039	−	0.393198i	−0.0691490	−	0.0399232i	−0.534176	+	0.845373i	$0.679378\pi$
$98$	8.00076	−	7.22194i	0.808198	−	0.729526i
$99$	−4.96459	−	4.82495i	−0.498960	−	0.484926i
$100$	0.497934			0.0497934
$101$	13.9764			1.39070			0.695352	−	0.718669i	$-0.255248\pi$
$101$	13.9764			1.39070			0.695352	+	0.718669i	$0.255248\pi$
$102$	9.22164	−	3.89701i	0.913079	−	0.385862i
$103$	−3.94047	+	2.27503i	−0.388266	+	0.224165i	−0.681408	−	0.731903i	$-0.738632\pi$
$103$	−3.94047	+	2.27503i	−0.388266	+	0.224165i	0.293143	+	0.956069i	$0.405299\pi$
$104$	−8.71567	+	2.41753i	−0.854642	+	0.237058i
$105$	8.76200	+	0.161473i	0.855084	+	0.0157582i
$106$	−8.31299	−	14.3985i	−0.807429	−	1.39851i
$107$	11.2737	+	6.50890i	1.08987	+	0.629239i	0.933543	−	0.358466i	$-0.116700\pi$
$107$	11.2737	+	6.50890i	1.08987	+	0.629239i	0.156331	+	0.987705i	$0.450033\pi$
$108$	0.292287	+	1.90436i	0.0281254	+	0.183247i
$109$	9.50574	−	16.4644i	0.910485	−	1.57701i	0.0971049	−	0.995274i	$-0.469042\pi$
$109$	9.50574	−	16.4644i	0.910485	−	1.57701i	0.813380	−	0.581732i	$-0.197625\pi$
$110$	6.79491			0.647869
$111$	7.75776	+	0.965095i	0.736334	+	0.0916027i
$112$	12.1138	−	1.28082i	1.14464	−	0.121026i
$113$	1.86352	+	1.07591i	0.175306	+	0.101213i	0.585085	−	0.810972i	$-0.301061\pi$
$113$	1.86352	+	1.07591i	0.175306	+	0.101213i	−0.409780	+	0.912185i	$0.634394\pi$
$114$	−12.7956	−	1.59182i	−1.19841	−	0.149087i
$115$			0.387678i			0.0361511i
$116$	0.0846191	+	0.0488549i	0.00785669	+	0.00453606i
$117$	−9.48960	−	5.19109i	−0.877314	−	0.479916i
$118$			6.00539i			0.552841i
$119$	4.03402	−	9.07573i	0.369798	−	0.831971i
$120$	6.62794	+	5.01110i	0.605045	+	0.457449i
$121$	5.67474			0.515886
$122$	−8.34829	+	14.4597i	−0.755819	+	1.30912i
$123$	−12.2673	+	16.2254i	−1.10611	+	1.46300i
$124$			0.757415i			0.0680179i
$125$	12.1299			1.08493
$126$	9.61114	+	7.54888i	0.856228	+	0.672507i
$127$	7.97146	+	13.8070i	0.707353	+	1.22517i	0.965836	+	0.259155i	$0.0834441\pi$
$127$	7.97146	+	13.8070i	0.707353	+	1.22517i	−0.258483	+	0.966016i	$0.583223\pi$
$128$	11.6133	+	6.70495i	1.02648	+	0.592640i
$129$	6.90397	+	0.858881i	0.607861	+	0.0756202i
$130$	10.2303	−	2.83766i	0.897260	−	0.248880i
$131$	−10.9573	−	18.9785i	−0.957341	−	1.65816i	−0.728918	−	0.684601i	$-0.759976\pi$
$131$	−10.9573	−	18.9785i	−0.957341	−	1.65816i	−0.228423	−	0.973562i	$-0.573357\pi$
$132$	1.18217	+	0.893787i	0.102895	+	0.0777942i
$133$	−10.3442	+	7.52534i	−0.896958	+	0.652530i
$134$	−7.74356	−	4.47075i	−0.668942	−	0.386214i
$135$	1.50749	+	9.82185i	0.129744	+	0.845330i
$136$	8.15525	−	4.70844i	0.699307	−	0.403745i
$137$	−4.77251	+	2.75541i	−0.407743	+	0.235411i	−0.689820	−	0.723981i	$-0.742310\pi$
$137$	−4.77251	+	2.75541i	−0.407743	+	0.235411i	0.282076	+	0.959392i	$0.408977\pi$
$138$	−0.326055	+	0.431257i	−0.0277556	+	0.0367110i
$139$	−6.44679	−	3.72206i	−0.546810	−	0.315701i	0.201025	−	0.979586i	$-0.435573\pi$
$139$	−6.44679	−	3.72206i	−0.546810	−	0.315701i	−0.747834	+	0.663886i	$0.768906\pi$
$140$	−1.86563	+	0.197258i	−0.157674	+	0.0166713i
$141$	10.0544	−	13.2985i	0.846734	−	1.11993i
$142$	−1.56998	−	2.71929i	−0.131750	−	0.228198i
$143$	−8.01764	+	2.22391i	−0.670469	+	0.185973i
$144$	3.76481	+	13.2893i	0.313734	+	1.10744i
$145$	0.436429	+	0.251972i	0.0362434	+	0.0209252i
$146$	4.01140	+	6.94795i	0.331986	+	0.575016i
$147$	12.0786	−	1.05246i	0.996225	−	0.0868051i
$148$	−1.67353			−0.137563
$149$		−	10.3526i		−	0.848119i	−0.905634	−	0.424059i	$-0.860605\pi$
$149$		−	10.3526i		−	0.848119i	0.905634	−	0.424059i	$-0.139395\pi$
$150$	2.85681	+	2.15992i	0.233258	+	0.176356i
$151$	1.59223	−	2.75782i	0.129574	−	0.224429i	−0.793938	−	0.607999i	$-0.791972\pi$
$151$	1.59223	−	2.75782i	0.129574	−	0.224429i	0.923512	+	0.383571i	$0.125306\pi$
$152$	−12.1286			−0.983762
$153$	10.9184	+	2.75929i	0.882702	+	0.223075i
$154$	9.34870	−	0.988462i	0.753340	−	0.0796526i
$155$			3.90642i			0.313771i
$156$	2.15312	+	0.851982i	0.172387	+	0.0682132i
$157$	−16.5406	−	9.54971i	−1.32008	−	0.762150i	−0.336341	−	0.941740i	$-0.609189\pi$
$157$	−16.5406	−	9.54971i	−1.32008	−	0.762150i	−0.983741	+	0.179590i	$0.942523\pi$
$158$		−	6.83398i		−	0.543682i
$159$	2.30888	−	18.5595i	0.183106	−	1.47187i
$160$	−3.43146	−	1.98116i	−0.271281	−	0.156624i
$161$	0.0563958	+	0.533382i	0.00444461	+	0.0420364i
$162$	−6.58368	+	12.1938i	−0.517263	+	0.958035i
$163$	22.0457			1.72675			0.863377	−	0.504559i	$-0.168345\pi$
$163$	22.0457			1.72675			0.863377	+	0.504559i	$0.168345\pi$
$164$	2.17722	−	3.77105i	0.170012	−	0.294470i
$165$	6.09711	+	4.60977i	0.474660	+	0.358870i
$166$	5.59431	+	3.22987i	0.434202	+	0.250687i
$167$	−9.61248	−	16.6493i	−0.743836	−	1.28836i	−0.950736	−	0.310000i	$-0.899671\pi$
$167$	−9.61248	−	16.6493i	−0.743836	−	1.28836i	0.206900	−	0.978362i	$-0.433662\pi$
$168$	9.84794	+	5.93029i	0.759785	+	0.457532i
$169$	−11.1425	+	6.69659i	−0.857117	+	0.515122i
$170$	−9.57252	+	5.52670i	−0.734179	+	0.423878i
$171$	−10.4016	−	10.1090i	−0.795431	−	0.773057i
$172$	−1.48935			−0.113562
$173$	3.79789			0.288748			0.144374	−	0.989523i	$-0.453883\pi$
$173$	3.79789			0.288748			0.144374	+	0.989523i	$0.453883\pi$
$174$	0.273568	+	0.647354i	0.0207391	+	0.0490757i
$175$	3.53333	−	0.373588i	0.267095	−	0.0282406i
$176$	9.20120	+	5.31232i	0.693567	+	0.400431i
$177$	−4.07414	+	5.38867i	−0.306231	+	0.405037i
$178$	15.8636	−	9.15883i	1.18902	−	0.686483i
$179$			20.1066i			1.50284i	0.659825	+	0.751420i	$0.270631\pi$
$179$			20.1066i			1.50284i	−0.659825	+	0.751420i	$0.729369\pi$
$180$	−0.579814	−	2.04667i	−0.0432168	−	0.152550i
$181$		−	16.8581i		−	1.25305i	−0.779399	−	0.626527i	$-0.784476\pi$
$181$		−	16.8581i		−	1.25305i	0.779399	−	0.626527i	$-0.215524\pi$
$182$	13.6625	−	5.39239i	1.01273	−	0.399710i
$183$	−17.3006	+	7.31113i	−1.27890	+	0.540455i
$184$	−0.254272	+	0.440411i	−0.0187451	+	0.0324675i
$185$	−8.63133			−0.634588
$186$	−3.28548	+	4.34554i	−0.240903	+	0.318631i
$187$	7.50211	−	4.33134i	0.548608	−	0.316739i
$188$	−1.78446	+	3.09078i	−0.130145	+	0.225418i
$189$	3.50286	+	13.2940i	0.254796	+	0.966995i
$190$	14.2364			1.03282
$191$		−	9.61215i		−	0.695511i	−0.937585	−	0.347756i	$-0.886944\pi$
$191$		−	9.61215i		−	0.695511i	0.937585	−	0.347756i	$-0.113056\pi$
$192$	4.05741	+	9.60120i	0.292818	+	0.692907i
$193$	−22.4635			−1.61696			−0.808480	−	0.588524i	$-0.799709\pi$
$193$	−22.4635			−1.61696			−0.808480	+	0.588524i	$0.799709\pi$
$194$	0.605421	+	1.04862i	0.0434667	+	0.0752865i
$195$	11.1048	+	4.39415i	0.795235	+	0.314672i
$196$	−2.53811	+	0.542789i	−0.181293	+	0.0387706i
$197$	−1.98684	+	1.14711i	−0.141557	+	0.0817279i	−0.569106	−	0.822264i	$-0.692710\pi$
$197$	−1.98684	+	1.14711i	−0.141557	+	0.0817279i	0.427549	+	0.903992i	$0.359377\pi$
$198$	2.90546	+	10.2559i	0.206482	+	0.728856i
$199$	−16.8067	+	9.70337i	−1.19140	+	0.687854i	−0.958624	−	0.284677i	$-0.908114\pi$
$199$	−16.8067	+	9.70337i	−1.19140	+	0.687854i	−0.232774	+	0.972531i	$0.574780\pi$
$200$	2.91746	+	1.68439i	0.206295	+	0.119105i
$201$	−3.91532	−	9.26497i	−0.276165	−	0.653501i
$202$	−18.6368	−	10.7600i	−1.31128	−	0.757070i
$203$	0.637110	+	0.283185i	0.0447164	+	0.0198757i
$204$	−2.39238	−	0.297621i	−0.167500	−	0.0208377i
$205$	11.2291	−	19.4495i	0.784278	−	1.35841i
$206$	7.00589			0.488123
$207$	−0.585142	+	0.165769i	−0.0406702	+	0.0115217i
$208$	16.0717	+	4.15559i	1.11437	+	0.288138i
$209$	−11.1573			−0.771764
$210$	−11.5594	−	6.96090i	−0.797673	−	0.480348i
$211$	−8.26159	−	14.3095i	−0.568751	−	0.985106i	−0.996690	−	0.0812981i	$-0.974093\pi$
$211$	−8.26159	−	14.3095i	−0.568751	−	0.985106i	0.427939	−	0.903808i	$-0.359240\pi$
$212$			4.00372i			0.274977i
$213$	0.436052	−	3.50514i	0.0298778	−	0.240168i
$214$	−10.0220	−	17.3586i	−0.685088	−	1.18661i
$215$	−7.68141			−0.523868
$216$	−4.72945	+	12.1466i	−0.321798	+	0.826471i
$217$	0.568270	+	5.37460i	0.0385767	+	0.364852i
$218$	−25.3509	+	14.6363i	−1.71698	+	0.991297i
$219$	−1.11414	+	8.95583i	−0.0752865	+	0.605179i
$220$	−1.41707	−	0.818145i	−0.0955387	−	0.0551593i
$221$	9.48624	−	9.65421i	0.638113	−	0.649413i
$222$	−9.60159	−	7.25935i	−0.644416	−	0.487216i
$223$	−10.0146	+	5.78196i	−0.670631	+	0.387189i	−0.796316	−	0.604881i	$-0.793220\pi$
$223$	−10.0146	+	5.78196i	−0.670631	+	0.387189i	0.125685	+	0.992070i	$0.459887\pi$
$224$	−5.00934	−	2.22657i	−0.334701	−	0.148769i
$225$	1.09812	+	3.87621i	0.0732078	+	0.258414i
$226$	−1.65661	−	2.86933i	−0.110196	−	0.190865i
$227$	0.553482	+	0.958659i	0.0367359	+	0.0636284i	0.883809	−	0.467848i	$-0.154971\pi$
$227$	0.553482	+	0.958659i	0.0367359	+	0.0636284i	−0.847073	+	0.531477i	$0.821637\pi$
$228$	2.47683	+	1.87263i	0.164032	+	0.124018i
$229$	6.53576	−	3.77342i	0.431895	−	0.249355i	−0.268259	−	0.963347i	$-0.586448\pi$
$229$	6.53576	−	3.77342i	0.431895	−	0.249355i	0.700154	+	0.713992i	$0.253115\pi$
$230$	0.298460	−	0.516949i	0.0196799	−	0.0340866i
$231$	9.05923	+	5.45534i	0.596054	+	0.358935i
$232$	0.330529	+	0.572493i	0.0217003	+	0.0375860i
$233$	2.96925	−	1.71430i	0.194522	−	0.112307i	−0.399576	−	0.916700i	$-0.630843\pi$
$233$	2.96925	−	1.71430i	0.194522	−	0.112307i	0.594098	+	0.804393i	$0.297509\pi$
$234$	8.65746	+	14.2278i	0.565956	+	0.930100i
$235$	−9.20349	+	15.9409i	−0.600370	+	1.03987i
$236$	0.723082	−	1.25242i	0.0470686	−	0.0815253i
$237$	4.63627	−	6.13217i	0.301158	−	0.398327i
$238$	−12.3663	+	8.99637i	−0.801586	+	0.583148i
$239$		−	9.51846i		−	0.615698i	−0.951435	−	0.307849i	$-0.900391\pi$
$239$		−	9.51846i		−	0.615698i	0.951435	−	0.307849i	$-0.0996092\pi$
$240$	−5.93628	−	14.0472i	−0.383185	−	0.906746i
$241$	−7.58765	+	4.38073i	−0.488763	+	0.282188i	−0.724061	−	0.689736i	$-0.757727\pi$
$241$	−7.58765	+	4.38073i	−0.488763	+	0.282188i	0.235298	+	0.971923i	$0.424393\pi$
$242$	−7.56698	−	4.36880i	−0.486424	−	0.280837i
$243$	−14.1800	+	6.47510i	−0.909649	+	0.415378i
$244$	3.48205	−	2.01036i	0.222915	−	0.128700i
$245$	−13.0905	+	2.79947i	−0.836318	+	0.178852i
$246$	28.8493	−	12.1915i	1.83937	−	0.777304i
$247$	−16.7982	+	4.65945i	−1.06885	+	0.296474i
$248$	−2.56216	+	4.43779i	−0.162697	+	0.281800i
$249$	2.82861	+	6.69344i	0.179256	+	0.424180i
$250$	−16.1746	−	9.33840i	−1.02297	−	0.590612i
$251$	9.70748	−	16.8139i	0.612731	−	1.06128i	−0.378047	−	0.925786i	$-0.623404\pi$
$251$	9.70748	−	16.8139i	0.612731	−	1.06128i	0.990778	−	0.135495i	$-0.0432624\pi$
$252$	−1.09546	−	2.73154i	−0.0690076	−	0.172071i
$253$	−0.233907	+	0.405139i	−0.0147056	+	0.0254709i
$254$		−	24.5479i		−	1.54027i
$255$	−12.3389	−	1.53500i	−0.772690	−	0.0961255i
$256$	−4.30595	−	7.45812i	−0.269122	−	0.466132i
$257$	7.58876	−	13.1441i	0.473374	−	0.819907i	−0.526162	−	0.850384i	$-0.676369\pi$
$257$	7.58876	−	13.1441i	0.473374	−	0.819907i	0.999535	+	0.0304772i	$0.00970270\pi$
$258$	−8.54488	−	6.46042i	−0.531981	−	0.402208i
$259$	−11.8753	+	1.25561i	−0.737897	+	0.0780197i
$260$	−2.47519	−	0.639998i	−0.153505	−	0.0396910i
$261$	−0.193700	+	0.766466i	−0.0119898	+	0.0474431i
$262$			33.7426i			2.08462i
$263$		−	1.74892i		−	0.107843i	−0.998545	−	0.0539214i	$-0.982828\pi$
$263$		−	1.74892i		−	0.107843i	0.998545	−	0.0539214i	$-0.0171720\pi$
$264$	3.90300	+	9.23581i	0.240213	+	0.568425i
$265$			20.6495i			1.26849i
$266$	19.5870	−	2.07099i	1.20096	−	0.126980i
$267$	20.4479	+	2.54380i	1.25139	+	0.155678i
$268$	1.07661	+	1.86473i	0.0657641	+	0.113907i
$269$	6.32521	+	10.9556i	0.385655	+	0.667974i	0.991860	−	0.127334i	$-0.0406421\pi$
$269$	6.32521	+	10.9556i	0.385655	+	0.667974i	−0.606205	+	0.795309i	$0.707309\pi$
$270$	5.55136	−	14.2575i	0.337845	−	0.867685i
$271$	9.31303	+	5.37688i	0.565726	+	0.326622i	0.755441	−	0.655217i	$-0.227423\pi$
$271$	9.31303	+	5.37688i	0.565726	+	0.326622i	−0.189714	+	0.981839i	$0.560756\pi$
$272$	−17.2833			−1.04795
$273$	15.9177	+	4.43022i	0.963383	+	0.268129i
$274$	8.48521			0.512610
$275$	2.68380	+	1.54949i	0.161839	+	0.0934380i
$276$	0.119924	−	0.0506791i	0.00721857	−	0.00305052i
$277$	−2.63447	−	4.56304i	−0.158290	−	0.274167i	0.775962	−	0.630780i	$-0.217265\pi$
$277$	−2.63447	−	4.56304i	−0.158290	−	0.274167i	−0.934252	+	0.356613i	$0.883931\pi$
$278$	5.73098	+	9.92635i	0.343721	+	0.595343i
$279$	−5.89616	+	1.67036i	−0.352994	+	0.100002i
$280$	−11.5982	−	5.15522i	−0.693126	−	0.308084i
$281$			20.3932i			1.21655i	0.793725	+	0.608277i	$0.208139\pi$
$281$			20.3932i			1.21655i	−0.793725	+	0.608277i	$0.791861\pi$
$282$	−23.6451	+	9.99228i	−1.40805	+	0.595032i
$283$			0.854407i			0.0507892i	0.999678	+	0.0253946i	$0.00808422\pi$
$283$			0.854407i			0.0507892i	−0.999678	+	0.0253946i	$0.991916\pi$
$284$			0.756139i			0.0448686i
$285$	12.7744	+	9.65819i	0.756691	+	0.572102i
$286$	12.4032	+	3.20705i	0.733419	+	0.189637i
$287$	12.6202	−	28.3928i	0.744945	−	1.67598i
$288$	1.52299	−	6.02641i	0.0897429	−	0.355110i
$289$	1.45413	−	2.51863i	0.0855373	−	0.148155i
$290$	−0.387971	−	0.671985i	−0.0227824	−	0.0394603i
$291$	−0.168151	+	1.35166i	−0.00985721	+	0.0792356i
$292$		−	1.93198i		−	0.113061i
$293$	−14.6836	+	25.4328i	−0.857828	+	1.48580i	0.0161693	+	0.999869i	$0.494853\pi$
$293$	−14.6836	+	25.4328i	−0.857828	+	1.48580i	−0.873997	+	0.485932i	$0.838480\pi$
$294$	−16.9164	−	7.89552i	−0.986587	−	0.460476i
$295$	3.72934	−	6.45941i	0.217131	−	0.376082i
$296$	−9.80541	−	5.66115i	−0.569928	−	0.329048i
$297$	−4.35067	+	11.1738i	−0.252451	+	0.648369i
$298$	−7.97014	+	13.8047i	−0.461698	+	0.799684i
$299$	−0.182975	+	0.707656i	−0.0105817	+	0.0409248i
$300$	−0.335718	−	0.794423i	−0.0193827	−	0.0458660i
$301$	−10.5684	+	1.11742i	−0.609151	+	0.0644071i
$302$	−4.24632	+	2.45161i	−0.244348	+	0.141075i
$303$	−9.42321	−	22.2985i	−0.541349	−	1.28102i
$304$	19.2780	+	11.1301i	1.10567	+	0.638358i
$305$	17.9589	−	10.3686i	1.02832	−	0.593703i
$306$	−12.4349	−	12.0851i	−0.710855	−	0.690860i
$307$		−	11.3469i		−	0.647601i	−0.946125	−	0.323801i	$-0.895039\pi$
$307$		−	11.3469i		−	0.647601i	0.946125	−	0.323801i	$-0.104961\pi$
$308$	−2.06867	−	0.919493i	−0.117874	−	0.0523930i
$309$	6.28642	+	4.75290i	0.357622	+	0.270383i
$310$	3.00743	−	5.20901i	0.170810	−	0.295852i
$311$	6.43447	−	11.1448i	0.364865	−	0.631965i	−0.623889	−	0.781513i	$-0.714448\pi$
$311$	6.43447	−	11.1448i	0.364865	−	0.631965i	0.988755	+	0.149548i	$0.0477818\pi$
$312$	9.73332	+	12.2754i	0.551041	+	0.694955i
$313$	22.4169	−	12.9424i	1.26708	−	0.731548i	0.292644	−	0.956221i	$-0.405465\pi$
$313$	22.4169	−	12.9424i	1.26708	−	0.731548i	0.974434	+	0.224673i	$0.0721315\pi$
$314$	14.7040	+	25.4681i	0.829796	+	1.43725i
$315$	−5.64992	−	14.0881i	−0.318337	−	0.793775i
$316$	−0.822849	+	1.42522i	−0.0462889	+	0.0801747i
$317$	25.8499	−	14.9244i	1.45187	−	0.838240i	0.453287	−	0.891365i	$-0.350251\pi$
$317$	25.8499	−	14.9244i	1.45187	−	0.838240i	0.998588	+	0.0531246i	$0.0169181\pi$
$318$	−17.3672	+	22.9707i	−0.973902	+	1.28813i
$319$	0.304057	+	0.526643i	0.0170240	+	0.0294863i
$320$	−5.75417	−	9.96652i	−0.321668	−	0.557145i
$321$	2.78353	−	22.3750i	0.155362	−	1.24885i
$322$	0.335432	−	0.754655i	0.0186929	−	0.0420553i
$323$	15.7181	−	9.07485i	0.874579	−	0.504938i
$324$	2.84122	−	1.75029i	0.157845	−	0.0972382i
$325$	4.68779	+	1.21210i	0.260032	+	0.0672351i
$326$	−29.3969	−	16.9723i	−1.62814	−	0.940008i
$327$	−32.6770	−	4.06514i	−1.80704	−	0.224803i
$328$	25.5132	−	14.7300i	1.40873	−	0.813330i
$329$	−10.3436	+	23.2710i	−0.570260	+	1.28297i
$330$	−4.58128	−	10.8409i	−0.252191	−	0.596770i
$331$	18.0270			0.990852			0.495426	−	0.868650i	$-0.335012\pi$
$331$	18.0270			0.990852			0.495426	+	0.868650i	$0.335012\pi$
$332$	−0.777789	−	1.34717i	−0.0426867	−	0.0739356i
$333$	−3.69071	−	13.0277i	−0.202249	−	0.713914i
$334$			29.6014i			1.61971i
$335$	5.55266	+	9.61749i	0.303374	+	0.525460i
$336$	−10.2108	−	18.4632i	−0.557046	−	1.00725i
$337$	3.48637			0.189915			0.0949574	−	0.995481i	$-0.469729\pi$
$337$	3.48637			0.189915			0.0949574	+	0.995481i	$0.469729\pi$
$338$	20.0135	−	0.351307i	1.08859	−	0.0191086i
$339$	0.460112	−	3.69854i	0.0249899	−	0.200877i
$340$	2.66178			0.144355
$341$	−2.35696	+	4.08237i	−0.127636	+	0.221073i
$342$	6.08741	+	21.4878i	0.329169	+	1.16192i
$343$	−17.6031	+	5.75590i	−0.950479	+	0.310789i
$344$	−8.72627	−	5.03811i	−0.470489	−	0.271637i
$345$	0.618516	−	0.261381i	0.0332998	−	0.0140723i
$346$	−5.06430	−	2.92388i	−0.272258	−	0.157188i
$347$	20.7292	−	11.9680i	1.11280	−	0.642476i	0.173248	−	0.984878i	$-0.444574\pi$
$347$	20.7292	−	11.9680i	1.11280	−	0.642476i	0.939554	+	0.342402i	$0.111241\pi$
$348$	0.0208928	−	0.167944i	0.00111997	−	0.00900272i
$349$	5.13216	−	2.96305i	0.274718	−	0.158609i	−0.356312	−	0.934367i	$-0.615966\pi$
$349$	5.13216	−	2.96305i	0.274718	−	0.158609i	0.631030	+	0.775759i	$0.282633\pi$
$350$	−4.99913	−	2.22204i	−0.267215	−	0.118773i
$351$	−1.88396	+	18.6400i	−0.100558	+	0.994931i
$352$	−2.39068	−	4.14078i	−0.127424	−	0.220704i
$353$	9.49437			0.505334			0.252667	−	0.967553i	$-0.418692\pi$
$353$	9.49437			0.505334			0.252667	+	0.967553i	$0.418692\pi$
$354$	9.58123	−	4.04897i	0.509237	−	0.215200i
$355$			3.89984i			0.206982i
$356$	−4.41110			−0.233788
$357$	−17.1996	−	0.316968i	−0.910299	−	0.0167757i
$358$	15.4794	−	26.8112i	0.818114	−	1.41701i
$359$	−31.0183	+	17.9084i	−1.63708	+	0.945171i	−0.655255	+	0.755408i	$0.727439\pi$
$359$	−31.0183	+	17.9084i	−1.63708	+	0.945171i	−0.981830	+	0.189764i	$0.939228\pi$
$360$	3.52620	−	13.9531i	0.185847	−	0.735391i
$361$	−4.37623			−0.230328
$362$	−12.9785	+	22.4795i	−0.682136	+	1.18149i
$363$	−3.82604	−	9.05370i	−0.200815	−	0.475196i
$364$	−3.49856	−	0.520466i	−0.183375	−	0.0272798i
$365$		−	9.96431i		−	0.521556i
$366$	28.6981	+	3.57015i	1.50007	+	0.186615i
$367$			5.58714i			0.291647i	0.989311	+	0.145823i	$0.0465831\pi$
$367$			5.58714i			0.291647i	−0.989311	+	0.145823i	$0.953417\pi$
$368$	0.808309	−	0.466678i	0.0421360	−	0.0243273i
$369$	34.1576	+	8.63226i	1.77817	+	0.449377i
$370$	11.5095	+	6.64499i	0.598348	+	0.345456i
$371$	3.00390	+	28.4103i	0.155955	+	1.47499i
$372$	1.20841	−	0.510666i	0.0626531	−	0.0264768i
$373$	9.69784			0.502135			0.251068	−	0.967970i	$-0.419218\pi$
$373$	9.69784			0.502135			0.251068	+	0.967970i	$0.419218\pi$
$374$	−13.3382			−0.689704
$375$	−8.17824	−	19.3525i	−0.422322	−	0.999357i
$376$	−20.9108	+	12.0728i	−1.07839	+	0.622610i
$377$	0.677720	+	0.665928i	0.0349043	+	0.0342970i
$378$	5.56372	−	20.4236i	0.286167	−	1.05048i
$379$	5.82515	+	10.0895i	0.299218	+	0.518261i	0.975957	−	0.217962i	$-0.0699409\pi$
$379$	5.82515	+	10.0895i	0.299218	+	0.518261i	−0.676739	+	0.736223i	$0.736608\pi$
$380$	−2.96898	−	1.71414i	−0.152306	−	0.0879337i
$381$	16.6536	−	22.0269i	0.853192	−	1.12847i
$382$	−7.40009	+	12.8173i	−0.378621	+	0.655792i
$383$	30.7820			1.57289			0.786443	−	0.617663i	$-0.211920\pi$
$383$	30.7820			1.57289			0.786443	+	0.617663i	$0.211920\pi$
$384$	2.86738	−	23.0490i	0.146325	−	1.17621i
$385$	−10.6693	−	4.74235i	−0.543759	−	0.241692i
$386$	29.9540	+	17.2939i	1.52462	+	0.880238i
$387$	−3.28452	−	11.5939i	−0.166962	−	0.589353i
$388$		−	0.291584i		−	0.0148029i
$389$	−6.92484	−	3.99806i	−0.351103	−	0.202710i	0.314068	−	0.949401i	$-0.398308\pi$
$389$	−6.92484	−	3.99806i	−0.351103	−	0.202710i	−0.665171	+	0.746691i	$0.731641\pi$
$390$	−11.4248	−	14.4086i	−0.578519	−	0.729610i
$391$		−	0.761002i		−	0.0384855i
$392$	−16.7072	−	5.40555i	−0.843841	−	0.273022i
$393$	−22.8915	+	30.2774i	−1.15472	+	1.52729i
$394$	3.53248			0.177964
$395$	−4.24390	+	7.35065i	−0.213534	+	0.369851i
$396$	0.628938	−	2.48869i	0.0316053	−	0.125061i
$397$			15.4304i			0.774431i	0.921989	+	0.387216i	$0.126563\pi$
$397$			15.4304i			0.774431i	−0.921989	+	0.387216i	$0.873437\pi$
$398$	29.8813			1.49781
$399$	18.9805	+	11.4298i	0.950215	+	0.572206i
$400$	−3.09146	−	5.35456i	−0.154573	−	0.267728i
$401$	16.3049	+	9.41364i	0.814228	+	0.470095i	0.848422	−	0.529320i	$-0.177553\pi$
$401$	16.3049	+	9.41364i	0.814228	+	0.470095i	−0.0341939	+	0.999415i	$0.510886\pi$
$402$	−1.91192	+	15.3687i	−0.0953578	+	0.766519i
$403$	−1.84374	+	7.13067i	−0.0918433	+	0.355204i
$404$	2.59112	+	4.48796i	0.128913	+	0.223284i
$405$	14.6538	−	9.02722i	0.728152	−	0.448566i
$406$	−0.631539	−	0.868104i	−0.0313428	−	0.0430833i
$407$	−9.02010	−	5.20776i	−0.447110	−	0.258139i
$408$	−13.0105	−	9.83667i	−0.644114	−	0.486988i
$409$	21.7675	−	12.5675i	1.07633	−	0.621422i	0.146429	−	0.989221i	$-0.453222\pi$
$409$	21.7675	−	12.5675i	1.07633	−	0.621422i	0.929905	+	0.367799i	$0.119889\pi$
$410$	−29.9470	+	17.2899i	−1.47898	+	0.853888i
$411$	7.61383	+	5.75649i	0.375562	+	0.283947i
$412$	−1.46107	−	0.843547i	−0.0719816	−	0.0415586i
$413$	4.19132	−	9.42962i	0.206241	−	0.464001i
$414$	0.907877	+	0.229438i	0.0446197	+	0.0112762i
$415$	−4.01150	−	6.94812i	−0.196917	−	0.341070i
$416$	−5.32864	−	5.23592i	−0.261258	−	0.256712i
$417$	−1.59174	+	12.7950i	−0.0779479	+	0.626571i
$418$	14.8777	+	8.58962i	0.727690	+	0.420132i
$419$	4.26159	+	7.38130i	0.208193	+	0.360600i	0.951145	−	0.308744i	$-0.0999086\pi$
$419$	4.26159	+	7.38130i	0.208193	+	0.360600i	−0.742953	+	0.669344i	$0.766575\pi$
$420$	1.57256	+	2.84350i	0.0767331	+	0.138748i
$421$	−30.4095			−1.48207			−0.741035	−	0.671466i	$-0.765665\pi$
$421$	−30.4095			−1.48207			−0.741035	+	0.671466i	$0.765665\pi$
$422$			25.4413i			1.23846i
$423$	−27.9958	−	7.07506i	−1.36120	−	0.344001i
$424$	−13.5437	+	23.4583i	−0.657738	+	1.13924i
$425$	−5.04117			−0.244533
$426$	−3.27995	+	4.33822i	−0.158914	+	0.210188i
$427$	23.2002	−	16.8780i	1.12274	−	0.816783i
$428$			4.82681i			0.233312i
$429$	8.95379	+	11.2922i	0.432293	+	0.545195i
$430$	10.2428	+	5.91367i	0.493950	+	0.285182i
$431$			18.8123i			0.906156i	0.891471	+	0.453078i	$0.149674\pi$
$431$			18.8123i			0.906156i	−0.891471	+	0.453078i	$0.850326\pi$
$432$	18.6639	−	14.9664i	0.897968	−	0.720074i
$433$	9.56781	+	5.52398i	0.459800	+	0.265466i	0.711960	−	0.702220i	$-0.247808\pi$
$433$	9.56781	+	5.52398i	0.459800	+	0.265466i	−0.252160	+	0.967685i	$0.581141\pi$
$434$	3.37997	−	7.60426i	0.162244	−	0.365016i
$435$	0.107756	−	0.866181i	0.00516651	−	0.0415302i
$436$	7.04918			0.337595
$437$	−0.490073	+	0.848831i	−0.0234434	+	0.0406051i
$438$	8.38045	−	11.0844i	0.400433	−	0.529634i
$439$	20.4191	+	11.7889i	0.974548	+	0.562656i	0.900620	−	0.434608i	$-0.143113\pi$
$439$	20.4191	+	11.7889i	0.974548	+	0.562656i	0.0739284	+	0.997264i	$0.476446\pi$
$440$	−5.53519	−	9.58722i	−0.263880	−	0.457053i
$441$	−9.82279	−	18.5611i	−0.467752	−	0.883860i
$442$	−20.0819	+	5.57027i	−0.955198	+	0.264951i
$443$	−33.9963	+	19.6278i	−1.61521	+	0.932543i	−0.627076	+	0.778958i	$0.715748\pi$
$443$	−33.9963	+	19.6278i	−1.61521	+	0.932543i	−0.988136	+	0.153584i	$0.950918\pi$
$444$	1.12833	+	2.67001i	0.0535482	+	0.126713i
$445$	−22.7505			−1.07848
$446$	17.8054			0.843109
$447$	−16.5169	+	6.97996i	−0.781225	+	0.330141i
$448$	−9.36665	−	12.8753i	−0.442533	−	0.608299i
$449$	−23.1182	−	13.3473i	−1.09101	−	0.629898i	−0.157168	−	0.987572i	$-0.550237\pi$
$449$	−23.1182	−	13.3473i	−1.09101	−	0.629898i	−0.933846	+	0.357674i	$0.883570\pi$
$450$	1.51988	−	6.01413i	0.0716480	−	0.283509i
$451$	23.4699	−	13.5503i	1.10515	−	0.638060i
$452$			0.797861i			0.0375282i
$453$	−5.47346	−	0.680919i	−0.257165	−	0.0319924i
$454$		−	1.70443i		−	0.0799929i
$455$	−18.0441	−	2.68434i	−0.845920	−	0.125844i
$456$	8.17739	+	19.3505i	0.382942	+	0.906169i
$457$	5.58912	−	9.68063i	0.261448	−	0.452841i	−0.705179	−	0.709029i	$-0.749133\pi$
$457$	5.58912	−	9.68063i	0.261448	−	0.452841i	0.966627	+	0.256188i	$0.0824667\pi$
$458$	−11.6201			−0.542973
$459$	−2.95917	−	19.2800i	−0.138122	−	0.899915i
$460$	−0.124487	+	0.0718726i	−0.00580423	+	0.00335108i
$461$	1.21945	−	2.11215i	0.0567954	−	0.0983725i	−0.836230	−	0.548379i	$-0.815245\pi$
$461$	1.21945	−	2.11215i	0.0567954	−	0.0983725i	0.893025	+	0.450007i	$0.148578\pi$
$462$	−7.88014	−	14.2488i	−0.366617	−	0.662916i
$463$	40.1909			1.86783			0.933915	−	0.357494i	$-0.116369\pi$
$463$	40.1909			1.86783			0.933915	+	0.357494i	$0.116369\pi$
$464$		−	1.21327i		−	0.0563249i
$465$	6.23245	−	2.63380i	0.289023	−	0.122139i
$466$	−5.27912			−0.244551
$467$	2.74438	+	4.75341i	0.126995	+	0.219961i	0.922511	−	0.385971i	$-0.126134\pi$
$467$	2.74438	+	4.75341i	0.126995	+	0.219961i	−0.795516	+	0.605932i	$0.792800\pi$
$468$	−0.0923951	−	4.00959i	−0.00427096	−	0.185343i
$469$	9.03863	+	12.4244i	0.417365	+	0.573704i
$470$	24.5448	−	14.1709i	1.13217	−	0.653657i
$471$	−4.08394	+	32.8281i	−0.188178	+	1.51264i
$472$	8.47325	−	4.89204i	0.390013	−	0.225174i
$473$	−8.02739	−	4.63462i	−0.369100	−	0.213100i
$474$	−10.9032	+	4.60762i	−0.500800	+	0.211635i
$475$	5.62299	+	3.24643i	0.258000	+	0.148957i
$476$	3.66218	−	0.387212i	0.167856	−	0.0177478i
$477$	−31.1673	+	8.82959i	−1.42705	+	0.404279i
$478$	−7.32796	+	12.6924i	−0.335173	+	0.580537i
$479$	−17.0285			−0.778050			−0.389025	−	0.921227i	$-0.627188\pi$
$479$	−17.0285			−0.778050			−0.389025	+	0.921227i	$0.627188\pi$
$480$	−0.847243	+	6.81043i	−0.0386712	+	0.310852i
$481$	−15.7554	−	4.07380i	−0.718384	−	0.185749i
$482$	13.4903			0.614468
$483$	0.812955	−	0.449594i	0.0369907	−	0.0204572i
$484$	1.05206	+	1.82221i	0.0478207	+	0.0828279i
$485$		−	1.50386i		−	0.0682870i
$486$	23.8933	+	2.28252i	1.08382	+	0.103537i
$487$	5.31841	+	9.21176i	0.241000	+	0.417424i	0.960999	−	0.276550i	$-0.0891912\pi$
$487$	5.31841	+	9.21176i	0.241000	+	0.417424i	−0.719999	+	0.693975i	$0.755858\pi$
$488$	27.2023			1.23139
$489$	−14.8637	−	35.1726i	−0.672161	−	1.59056i
$490$	19.6107	+	6.34496i	0.885921	+	0.286636i
$491$	4.91270	−	2.83635i	0.221707	−	0.128003i	−0.385033	−	0.922903i	$-0.625810\pi$
$491$	4.91270	−	2.83635i	0.221707	−	0.128003i	0.606740	+	0.794900i	$0.292477\pi$
$492$	−7.48441	−	0.931089i	−0.337423	−	0.0419767i
$493$	−0.856699	−	0.494615i	−0.0385838	−	0.0222764i
$494$	25.9868	+	6.71927i	1.16920	+	0.302314i
$495$	3.24379	−	12.8356i	0.145798	−	0.576916i
$496$	8.14490	−	4.70246i	0.365717	−	0.211147i
$497$	0.567313	+	5.36555i	0.0254475	+	0.240678i
$498$	1.38126	−	11.1030i	0.0618957	−	0.497538i
$499$	2.94413	+	5.09938i	0.131797	+	0.228280i	0.924369	−	0.381499i	$-0.124592\pi$
$499$	2.94413	+	5.09938i	0.131797	+	0.228280i	−0.792572	+	0.609778i	$0.791259\pi$
$500$	2.24879	+	3.89502i	0.100569	+	0.174191i
$501$	−20.0820	+	26.5615i	−0.897198	+	1.18668i
$502$	−25.8889	+	14.9470i	−1.15548	+	0.667115i
$503$	7.14545	−	12.3763i	0.318600	−	0.551831i	−0.661596	−	0.749860i	$-0.730121\pi$
$503$	7.14545	−	12.3763i	0.318600	−	0.551831i	0.980196	+	0.198029i	$0.0634541\pi$
$504$	2.82172	−	19.7101i	0.125689	−	0.877959i
$505$	13.3639	+	23.1469i	0.594685	+	1.03003i
$506$	0.623807	−	0.360155i	0.0277316	−	0.0160109i
$507$	18.1965	+	13.2622i	0.808137	+	0.588995i
$508$	−2.95570	+	5.11942i	−0.131138	+	0.227138i
$509$	−10.6611	+	18.4656i	−0.472545	+	0.818472i	−0.999506	−	0.0314171i	$-0.989998\pi$
$509$	−10.6611	+	18.4656i	−0.472545	+	0.818472i	0.526961	+	0.849889i	$0.323331\pi$
$510$	15.2715	+	11.5461i	0.676234	+	0.511272i
$511$	−1.44952	−	13.7093i	−0.0641229	−	0.606463i
$512$		−	13.5598i		−	0.599263i
$513$	−9.11534	+	23.4109i	−0.402452	+	1.03362i
$514$	−20.2385	+	11.6847i	−0.892680	+	0.515389i
$515$	−7.53555	−	4.35065i	−0.332056	−	0.191713i
$516$	1.00415	+	2.37616i	0.0442053	+	0.104605i
$517$	−19.2361	+	11.1059i	−0.846001	+	0.488439i
$518$	16.8018	+	7.46814i	0.738229	+	0.328131i
$519$	−2.56062	−	6.05930i	−0.112399	−	0.265974i
$520$	−12.3375	−	12.1228i	−0.541034	−	0.531621i
$521$	1.36848	−	2.37027i	0.0599540	−	0.103843i	−0.834491	−	0.551022i	$-0.814238\pi$
$521$	1.36848	−	2.37027i	0.0599540	−	0.103843i	0.894445	+	0.447179i	$0.147571\pi$
$522$	0.848367	−	0.872921i	0.0371320	−	0.0382067i
$523$	−6.20985	−	3.58526i	−0.271538	−	0.156773i	0.358048	−	0.933703i	$-0.383442\pi$
$523$	−6.20985	−	3.58526i	−0.271538	−	0.156773i	−0.629586	+	0.776931i	$0.716776\pi$
$524$	4.06279	−	7.03696i	0.177484	−	0.307411i
$525$	−2.97829	−	5.38533i	−0.129983	−	0.235035i
$526$	−1.34643	+	2.33209i	−0.0587073	+	0.101684i
$527$		−	7.66820i		−	0.334032i
$528$	2.27182	−	18.2616i	0.0988682	−	0.794736i
$529$	−11.4795	−	19.8830i	−0.499107	−	0.864478i
$530$	15.8974	−	27.5350i	0.690537	−	1.19605i
$531$	11.3442	+	2.86688i	0.492295	+	0.124412i
$532$	−4.33420	−	1.92648i	−0.187911	−	0.0835237i
$533$	29.6771	−	30.2026i	1.28546	−	1.30822i
$534$	−25.3079	−	19.1342i	−1.09518	−	0.828020i
$535$			24.8946i			1.07629i
$536$			14.5676i			0.629225i
$537$	32.0789	−	13.5563i	1.38431	−	0.584999i
$538$		−	19.4783i		−	0.839770i
$539$	−15.3691	−	4.97263i	−0.661996	−	0.214186i
$540$	−2.87441	+	2.30497i	−0.123695	+	0.0991900i
$541$	−8.19656	−	14.1969i	−0.352397	−	0.610370i	0.634272	−	0.773110i	$-0.281300\pi$
$541$	−8.19656	−	14.1969i	−0.352397	−	0.610370i	−0.986669	+	0.162740i	$0.947967\pi$
$542$	−8.27897	−	14.3396i	−0.355612	−	0.615938i
$543$	−26.8961	+	11.3661i	−1.15422	+	0.487767i
$544$	6.73588	+	3.88896i	0.288798	+	0.166738i
$545$	36.3566			1.55735
$546$	−17.8148	−	18.1620i	−0.762402	−	0.777262i
$547$	7.36008			0.314694			0.157347	−	0.987543i	$-0.449706\pi$
$547$	7.36008			0.314694			0.157347	+	0.987543i	$0.449706\pi$
$548$	−1.76958	−	1.02167i	−0.0755926	−	0.0436434i
$549$	23.3289	+	22.6727i	0.995655	+	0.967649i
$550$	−2.38581	−	4.13234i	−0.101731	−	0.176204i
$551$	0.637049	+	1.10340i	0.0271392	+	0.0470064i
$552$	0.874085	+	0.108739i	0.0372035	+	0.00462826i
$553$	−4.76961	+	10.7307i	−0.202825	+	0.456314i
$554$			8.11278i			0.344679i
$555$	5.81944	+	13.7708i	0.247021	+	0.584536i
$556$		−	2.76017i		−	0.117057i
$557$		−	41.1128i		−	1.74201i	−0.491278	−	0.871003i	$-0.663470\pi$
$557$		−	41.1128i		−	1.74201i	0.491278	−	0.871003i	$-0.336530\pi$
$558$	9.14819	+	2.31192i	0.387274	+	0.0978713i
$559$	−14.0214	−	3.62545i	−0.593043	−	0.153340i
$560$	13.7041	+	18.8374i	0.579103	+	0.796026i
$561$	−11.9685	−	9.04886i	−0.505310	−	0.382043i
$562$	15.7000	−	27.1932i	0.662266	−	1.14708i
$563$	−7.36906	−	12.7636i	−0.310569	−	0.537921i	0.667917	−	0.744236i	$-0.267186\pi$
$563$	−7.36906	−	12.7636i	−0.310569	−	0.537921i	−0.978486	+	0.206315i	$0.933853\pi$
$564$	6.13428	+	0.763127i	0.258300	+	0.0321335i
$565$			4.11502i			0.173120i
$566$	0.657780	−	1.13931i	0.0276486	−	0.0478887i
$567$	18.8480	−	14.5517i	0.791543	−	0.611114i
$568$	−2.55784	+	4.43031i	−0.107325	+	0.185892i
$569$	−20.8152	−	12.0176i	−0.872617	−	0.503806i	−0.00439981	−	0.999990i	$-0.501401\pi$
$569$	−20.8152	−	12.0176i	−0.872617	−	0.503806i	−0.868217	+	0.496185i	$0.834734\pi$
$570$	−9.59851	−	22.7133i	−0.402037	−	0.951357i
$571$	5.51532	−	9.55282i	0.230809	−	0.399773i	−0.727237	−	0.686386i	$-0.759196\pi$
$571$	5.51532	−	9.55282i	0.230809	−	0.399773i	0.958046	+	0.286613i	$0.0925294\pi$
$572$	−2.20053	−	2.16224i	−0.0920088	−	0.0904079i
$573$	−15.3356	+	6.48073i	−0.640654	+	0.270736i
$574$	−38.6871	+	28.1446i	−1.61477	+	1.17473i
$575$	0.235767	−	0.136120i	0.00983217	−	0.00567661i
$576$	12.5825	−	12.9467i	0.524272	−	0.539446i
$577$	−6.76920	−	3.90820i	−0.281805	−	0.162700i	0.352435	−	0.935836i	$-0.385354\pi$
$577$	−6.76920	−	3.90820i	−0.281805	−	0.162700i	−0.634240	+	0.773136i	$0.718687\pi$
$578$	−3.87803	+	2.23898i	−0.161305	+	0.0931293i
$579$	15.1454	+	35.8392i	0.629422	+	1.48942i
$580$			0.186855i			0.00775874i
$581$	−6.52993	−	8.97594i	−0.270907	−	0.372385i
$582$	1.26482	−	1.67291i	0.0524285	−	0.0693445i
$583$	−12.4590	+	21.5795i	−0.515997	+	0.893734i
$584$	6.53543	−	11.3197i	0.270438	−	0.468413i
$585$	−0.476534	−	20.6797i	−0.0197023	−	0.855002i
$586$	39.1598	−	22.6089i	1.61768	−	0.933966i
$587$	−2.43294	−	4.21397i	−0.100418	−	0.173929i	0.811439	−	0.584437i	$-0.198685\pi$
$587$	−2.43294	−	4.21397i	−0.100418	−	0.173929i	−0.911857	+	0.410508i	$0.865351\pi$
$588$	2.57724	+	3.68343i	0.106283	+	0.151902i
$589$	−4.93820	+	8.55321i	−0.203475	+	0.352429i
$590$	−9.94579	+	5.74220i	−0.409462	+	0.236403i
$591$	3.16971	+	2.39648i	0.130384	+	0.0985782i
$592$	10.3902	+	17.9964i	0.427035	+	0.739646i
$593$	−21.6766	−	37.5450i	−0.890152	−	1.54179i	−0.839692	−	0.543063i	$-0.817264\pi$
$593$	−21.6766	−	37.5450i	−0.890152	−	1.54179i	−0.0504606	−	0.998726i	$-0.516069\pi$
$594$	14.4037	−	11.5503i	0.590993	−	0.473913i
$595$	18.8879	−	1.99707i	0.774330	−	0.0818719i
$596$	3.32432	−	1.91930i	0.136169	−	0.0786175i
$597$	26.8126	+	20.2719i	1.09737	+	0.829673i
$598$	0.788790	−	0.802757i	0.0322560	−	0.0328272i
$599$	17.2985	+	9.98730i	0.706798	+	0.408070i	0.809874	−	0.586604i	$-0.199535\pi$
$599$	17.2985	+	9.98730i	0.706798	+	0.408070i	−0.103076	+	0.994673i	$0.532869\pi$
$600$	0.720333	−	5.79028i	0.0294075	−	0.236387i
$601$	−13.3976	+	7.73512i	−0.546500	+	0.315522i	−0.747709	−	0.664026i	$-0.768846\pi$
$601$	−13.3976	+	7.73512i	−0.546500	+	0.315522i	0.201209	+	0.979548i	$0.435513\pi$
$602$	14.9527	+	6.64623i	0.609425	+	0.270880i
$603$	−12.1419	+	12.4933i	−0.494456	+	0.508767i
$604$	1.18075			0.0480441
$605$	5.42605	+	9.39819i	0.220600	+	0.382091i
$606$	−4.60152	+	36.9886i	−0.186924	+	1.50256i
$607$		−	10.2908i		−	0.417693i	−0.977948	−	0.208846i	$-0.933029\pi$
$607$		−	10.2908i		−	0.417693i	0.977948	−	0.208846i	$-0.0669708\pi$
$608$	−5.00886	−	8.67559i	−0.203136	−	0.351842i
$609$	0.0222510	−	1.20740i	0.000901654	−	0.0489263i
$610$	−31.9297			−1.29280
$611$	−24.3236	+	24.7543i	−0.984026	+	1.00145i
$612$	1.13816	+	4.01756i	0.0460074	+	0.162400i
$613$	32.6231			1.31763			0.658817	−	0.752303i	$-0.271057\pi$
$613$	32.6231			1.31763			0.658817	+	0.752303i	$0.271057\pi$
$614$	−8.73560	+	15.1305i	−0.352540	+	0.610618i
$615$	−38.6013	−	4.80215i	−1.55656	−	0.193642i
$616$	−9.01019	−	12.3853i	−0.363031	−	0.499016i
$617$	−37.9111	−	21.8880i	−1.52625	−	0.881178i	−0.999515	−	0.0311459i	$-0.990084\pi$
$617$	−37.9111	−	21.8880i	−1.52625	−	0.881178i	−0.526731	−	0.850032i	$-0.676582\pi$
$618$	−4.72353	−	11.1775i	−0.190008	−	0.449623i
$619$	4.18956	+	2.41884i	0.168393	+	0.0972215i	0.581828	−	0.813312i	$-0.302338\pi$
$619$	4.18956	+	2.41884i	0.168393	+	0.0972215i	−0.413435	+	0.910534i	$0.635671\pi$
$620$	−1.25439	+	0.724221i	−0.0503774	+	0.0290854i
$621$	0.658989	+	0.821793i	0.0264443	+	0.0329774i
$622$	−17.1601	+	9.90738i	−0.688056	+	0.397250i
$623$	−31.3010	+	3.30954i	−1.25405	+	0.132594i
$624$	−4.20594	−	28.4432i	−0.168372	−	1.13864i
$625$	8.24099	+	14.2738i	0.329640	+	0.570953i
$626$	−39.8558			−1.59296
$627$	7.52248	+	17.8007i	0.300419	+	0.710892i
$628$		−	7.08179i		−	0.282594i
$629$	16.9431			0.675565
$630$	−3.31209	+	23.1355i	−0.131957	+	0.921739i
$631$	9.28534	−	16.0827i	0.369644	−	0.640242i	−0.619866	−	0.784708i	$-0.712813\pi$
$631$	9.28534	−	16.0827i	0.369644	−	0.640242i	0.989510	+	0.144466i	$0.0461464\pi$
$632$	−9.64234	+	5.56701i	−0.383552	+	0.221444i
$633$	−17.2598	+	22.8286i	−0.686014	+	0.907357i
$634$	−45.9594			−1.82528
$635$	−15.2442	+	26.4038i	−0.604949	+	1.04780i
$636$	6.38769	−	2.69940i	0.253288	−	0.107038i
$637$	−25.2162	−	1.06832i	−0.999104	−	0.0423285i
$638$		−	0.936336i		−	0.0370699i
$639$	−5.88623	+	1.66755i	−0.232856	+	0.0659672i
$640$			25.6444i			1.01369i
$641$	−1.61326	+	0.931414i	−0.0637198	+	0.0367886i	−0.531521	−	0.847045i	$-0.678379\pi$
$641$	−1.61326	+	0.931414i	−0.0637198	+	0.0367886i	0.467802	+	0.883833i	$0.345046\pi$
$642$	−20.9375	+	27.6930i	−0.826337	+	1.09296i
$643$	8.43742	+	4.87135i	0.332739	+	0.192107i	0.657057	−	0.753841i	$-0.271801\pi$
$643$	8.43742	+	4.87135i	0.332739	+	0.192107i	−0.324317	+	0.945948i	$0.605135\pi$
$644$	−0.160819	+	0.116994i	−0.00633714	+	0.00461022i
$645$	5.17898	+	12.2552i	0.203922	+	0.482549i
$646$	−27.9457			−1.09951
$647$	1.73007			0.0680162			0.0340081	−	0.999422i	$-0.489173\pi$
$647$	1.73007			0.0680162			0.0340081	+	0.999422i	$0.489173\pi$
$648$	22.5679	−	0.643971i	0.886549	−	0.0252976i
$649$	7.79464	−	4.50024i	0.305966	−	0.176650i
$650$	−5.31778	−	5.22525i	−0.208580	−	0.204951i
$651$	8.19171	−	4.53032i	0.321058	−	0.177557i
$652$	4.08711	+	7.07909i	0.160064	+	0.277239i
$653$	−20.3586	−	11.7540i	−0.796693	−	0.459971i	0.0456203	−	0.998959i	$-0.485474\pi$
$653$	−20.3586	−	11.7540i	−0.796693	−	0.459971i	−0.842314	+	0.538988i	$0.818807\pi$
$654$	40.4435	+	30.5776i	1.58147	+	1.19568i
$655$	20.9541	−	36.2936i	0.818746	−	1.41811i
$656$	−54.0696			−2.11106
$657$	15.0396	−	4.26068i	0.586753	−	0.166225i
$658$	31.7082	−	23.0675i	1.23611	−	0.899264i
$659$	−11.6929	−	6.75090i	−0.455491	−	0.262978i	0.254655	−	0.967032i	$-0.418038\pi$
$659$	−11.6929	−	6.75090i	−0.455491	−	0.262978i	−0.710146	+	0.704054i	$0.751371\pi$
$660$	−0.349880	+	2.81246i	−0.0136191	+	0.109475i
$661$		−	4.19236i		−	0.163064i	−0.996671	−	0.0815320i	$-0.974019\pi$
$661$		−	4.19236i		−	0.163064i	0.996671	−	0.0815320i	$-0.0259813\pi$
$662$	−24.0381	−	13.8784i	−0.934266	−	0.539399i
$663$	−21.7985	−	8.62562i	−0.846585	−	0.334991i
$664$		−	10.5243i		−	0.408423i
$665$	−22.3539	−	9.93597i	−0.866848	−	0.385300i
$666$	−5.10824	+	20.2132i	−0.197940	+	0.783244i
$667$	0.0534218			0.00206850
$668$	3.56417	−	6.17332i	0.137902	−	0.238853i
$669$	15.9769	+	12.0794i	0.617701	+	0.467018i
$670$		−	17.0993i		−	0.660602i
$671$	25.0237			0.966030
$672$	−0.174950	+	9.49330i	−0.00674885	+	0.366212i
$673$	−6.96155	−	12.0578i	−0.268348	−	0.464792i	0.700087	−	0.714057i	$-0.253144\pi$
$673$	−6.96155	−	12.0578i	−0.268348	−	0.464792i	−0.968435	+	0.249265i	$0.919811\pi$
$674$	−4.64890	−	2.68404i	−0.179069	−	0.103386i
$675$	5.44388	−	4.36540i	0.209535	−	0.168024i
$676$	−4.21608	−	2.33647i	−0.162157	−	0.0898642i
$677$	12.3751	+	21.4343i	0.475614	+	0.823788i	0.999610	−	0.0279327i	$-0.00889242\pi$
$677$	12.3751	+	21.4343i	0.475614	+	0.823788i	−0.523995	+	0.851721i	$0.675559\pi$
$678$	−3.46092	+	4.57759i	−0.132916	+	0.175801i
$679$	−0.218769	−	2.06907i	−0.00839557	−	0.0794038i
$680$	15.5957	+	9.00418i	0.598067	+	0.345294i
$681$	1.15631	−	1.52940i	0.0443099	−	0.0586066i
$682$	6.28577	−	3.62909i	0.240695	−	0.138965i
$683$	10.8334	−	6.25466i	0.414528	−	0.239328i	−0.278205	−	0.960522i	$-0.589740\pi$
$683$	10.8334	−	6.25466i	0.414528	−	0.239328i	0.692734	+	0.721194i	$0.256406\pi$
$684$	1.31773	−	5.21420i	0.0503845	−	0.199370i
$685$	−9.12672	−	5.26931i	−0.348714	−	0.201330i
$686$	27.9042	+	5.87686i	1.06539	+	0.224380i
$687$	−10.4268	−	7.88327i	−0.397808	−	0.300766i
$688$	9.24671	+	16.0158i	0.352527	+	0.610595i
$689$	−9.74608	+	37.6930i	−0.371296	+	1.43599i
$690$	−1.02599	−	0.127637i	−0.0390587	−	0.00485905i
$691$	3.78731	+	2.18660i	0.144076	+	0.0831823i	0.570305	−	0.821433i	$-0.306825\pi$
$691$	3.78731	+	2.18660i	0.144076	+	0.0831823i	−0.426229	+	0.904615i	$0.640158\pi$
$692$	0.704101	+	1.21954i	0.0267659	+	0.0463599i
$693$	2.59573	−	18.1316i	0.0986036	−	0.688761i
$694$	−36.8551			−1.39900
$695$		−	14.2357i		−	0.539993i
$696$	0.690528	−	0.913327i	0.0261744	−	0.0346196i
$697$	−22.0425	+	38.1788i	−0.834921	+	1.44612i
$698$	−9.12464			−0.345373
$699$	−4.73699	−	3.58143i	−0.179169	−	0.135462i
$700$	0.775016	+	1.06533i	0.0292929	+	0.0402655i
$701$			36.4301i			1.37595i	0.725736	+	0.687973i	$0.241499\pi$
$701$			36.4301i			1.37595i	−0.725736	+	0.687973i	$0.758501\pi$
$702$	16.8625	−	23.4051i	0.636435	−	0.883370i
$703$	−18.8985	−	10.9111i	−0.712772	−	0.411519i
$704$		−	13.8872i		−	0.523395i
$705$	31.6380	+	3.93588i	1.19155	+	0.148234i
$706$	−12.6603	−	7.30941i	−0.476476	−	0.275093i
$707$	21.7538	+	29.9024i	0.818135	+	1.12460i
$708$	−2.48567	−	0.309227i	−0.0934172	−	0.0116215i
$709$	2.47450			0.0929318			0.0464659	−	0.998920i	$-0.485204\pi$
$709$	2.47450			0.0929318			0.0464659	+	0.998920i	$0.485204\pi$
$710$	3.00236	−	5.20024i	0.112677	−	0.195162i
$711$	−12.9094	−	3.26244i	−0.484139	−	0.122351i
$712$	−25.8451	−	14.9217i	−0.968588	−	0.559214i
$713$	0.207054	+	0.358629i	0.00775425	+	0.0134308i
$714$	22.6908	+	13.6641i	0.849181	+	0.511365i
$715$	−11.3494	−	11.1519i	−0.424443	−	0.417058i
$716$	−6.45643	+	3.72762i	−0.241288	+	0.139308i
$717$	−15.1861	+	6.41756i	−0.567136	+	0.239668i
$718$	55.1485			2.05812
$719$	−2.07634			−0.0774345			−0.0387172	−	0.999250i	$-0.512327\pi$
$719$	−2.07634			−0.0774345			−0.0387172	+	0.999250i	$0.512327\pi$
$720$	−18.4091	+	18.9419i	−0.686068	+	0.705924i
$721$	−11.0006	−	4.88959i	−0.409684	−	0.182098i
$722$	5.83548	+	3.36912i	0.217174	+	0.125386i
$723$	12.1049	+	9.15204i	0.450188	+	0.340368i
$724$	5.41331	−	3.12537i	0.201184	−	0.116154i
$725$		−	0.353887i		−	0.0131430i
$726$	−1.86832	+	15.0182i	−0.0693399	+	0.557378i
$727$		−	8.36821i		−	0.310360i	−0.987886	−	0.155180i	$-0.950404\pi$
$727$		−	8.36821i		−	0.310360i	0.987886	−	0.155180i	$-0.0495957\pi$
$728$	−18.7379	−	14.8843i	−0.694473	−	0.551649i
$729$	19.8911	+	18.2577i	0.736708	+	0.676211i
$730$	−7.67120	+	13.2869i	−0.283924	+	0.491771i
$731$	15.0784			0.557695
$732$	−5.55508	−	4.19996i	−0.205322	−	0.155235i
$733$	−31.2081	+	18.0180i	−1.15270	+	0.665510i	−0.949543	−	0.313637i	$-0.898453\pi$
$733$	−31.2081	+	18.0180i	−1.15270	+	0.665510i	−0.203154	+	0.979147i	$0.565119\pi$
$734$	4.30136	−	7.45018i	0.158766	−	0.274991i
$735$	13.2923	+	18.9975i	0.490293	+	0.700735i
$736$	−0.420034			−0.0154827
$737$			13.4009i			0.493629i
$738$	−38.9017	−	37.8075i	−1.43199	−	1.39171i
$739$	39.7187			1.46108			0.730539	−	0.682871i	$-0.239269\pi$
$739$	39.7187			1.46108			0.730539	+	0.682871i	$0.239269\pi$
$740$	−1.60019	−	2.77160i	−0.0588240	−	0.101886i
$741$	18.7596	+	23.6590i	0.689152	+	0.869136i
$742$	17.8666	−	40.1964i	0.655905	−	1.47565i
$743$	1.45158	−	0.838068i	0.0532531	−	0.0307457i	−0.473137	−	0.880989i	$-0.656878\pi$
$743$	1.45158	−	0.838068i	0.0532531	−	0.0307457i	0.526390	+	0.850243i	$0.323545\pi$
$744$	8.80768	+	1.09571i	0.322905	+	0.0401706i
$745$	17.1454	−	9.89890i	0.628159	−	0.362668i
$746$	−12.9316	−	7.46605i	−0.473459	−	0.273352i
$747$	8.77186	−	9.02574i	0.320946	−	0.330235i
$748$	2.78167	+	1.60600i	0.101708	+	0.0587211i
$749$	3.62144	+	34.2509i	0.132324	+	1.25150i
$750$	−3.99358	+	32.1017i	−0.145825	+	1.17219i
$751$	0.160307	−	0.277661i	0.00584970	−	0.0101320i	−0.863086	−	0.505057i	$-0.831471\pi$
$751$	0.160307	−	0.277661i	0.00584970	−	0.0101320i	0.868935	+	0.494925i	$0.164805\pi$
$752$	44.3158			1.61603
$753$	−33.3705	−	4.15141i	−1.21609	−	0.151286i
$754$	−0.391029	−	1.40974i	−0.0142404	−	0.0513396i
$755$	6.08980			0.221631
$756$	−3.61942	+	3.58941i	−0.131637	+	0.130546i
$757$	11.1148	+	19.2515i	0.403976	+	0.699707i	0.994202	−	0.107532i	$-0.0342947\pi$
$757$	11.1148	+	19.2515i	0.403976	+	0.699707i	−0.590226	+	0.807238i	$0.700961\pi$
$758$		−	17.9384i		−	0.651551i
$759$	0.804080	+	0.100031i	0.0291863	+	0.00363088i
$760$	−11.5971	−	20.0868i	−0.420671	−	0.728623i
$761$	36.7323			1.33155			0.665773	−	0.746154i	$-0.268102\pi$
$761$	36.7323			1.33155			0.665773	+	0.746154i	$0.268102\pi$
$762$	−39.1646	+	16.5507i	−1.41878	+	0.599570i
$763$	50.0208	−	5.28883i	1.81088	−	0.191469i
$764$	3.08655	−	1.78202i	0.111668	−	0.0644713i
$765$	5.87014	+	20.7208i	0.212235	+	0.749163i
$766$	−41.0462	−	23.6981i	−1.48306	−	0.856246i
$767$	9.85614	−	10.0307i	0.355885	−	0.362186i
$768$	−8.99580	+	11.8983i	−0.324608	+	0.429343i
$769$	36.7540	−	21.2199i	1.32538	−	0.765211i	0.340802	−	0.940135i	$-0.389301\pi$
$769$	36.7540	−	21.2199i	1.32538	−	0.765211i	0.984582	+	0.174924i	$0.0559680\pi$
$770$	10.5760	+	14.5377i	0.381134	+	0.523901i
$771$	−26.0871	−	3.24534i	−0.939505	−	0.116878i
$772$	−4.16457	−	7.21325i	−0.149886	−	0.259611i
$773$	1.46891	+	2.54423i	0.0528330	+	0.0915095i	0.891232	−	0.453547i	$-0.149842\pi$
$773$	1.46891	+	2.54423i	0.0528330	+	0.0915095i	−0.838399	+	0.545056i	$0.816508\pi$
$774$	−4.54605	+	17.9886i	−0.163405	+	0.646587i
$775$	2.37570	−	1.37161i	0.0853376	−	0.0492697i
$776$	0.986360	−	1.70843i	0.0354083	−	0.0613289i
$777$	10.0099	+	18.0998i	0.359102	+	0.649326i
$778$	6.15595	+	10.6624i	0.220702	+	0.382266i
$779$	49.1731	−	28.3901i	1.76181	−	1.01718i
$780$	0.647752	+	4.38052i	0.0231932	+	0.156848i
$781$	−2.35299	+	4.07549i	−0.0841965	+	0.145833i
$782$	−0.585871	+	1.01476i	−0.0209507	+	0.0362877i
$783$	1.35345	−	0.207732i	0.0483682	−	0.00742373i
$784$	21.5949	+	23.9237i	0.771247	+	0.854418i
$785$		−	36.5248i		−	1.30363i
$786$	53.8342	−	22.7500i	1.92020	−	0.811466i
$787$	−20.1988	+	11.6618i	−0.720009	+	0.415697i	−0.814756	−	0.579804i	$-0.803129\pi$
$787$	−20.1988	+	11.6618i	−0.720009	+	0.415697i	0.0947470	+	0.995501i	$0.469796\pi$
$788$	−0.736693	−	0.425330i	−0.0262436	−	0.0151517i
$789$	−2.79029	+	1.17916i	−0.0993369	+	0.0419792i
$790$	11.3181	−	6.53448i	0.402678	−	0.232486i
$791$	0.598616	+	5.66160i	0.0212843	+	0.201303i
$792$	12.1037	−	12.4540i	0.430085	−	0.442533i
$793$	37.6754	−	10.4503i	1.33789	−	0.371101i
$794$	11.8794	−	20.5757i	0.421584	−	0.730205i
$795$	32.9449	−	13.9223i	1.16844	−	0.493774i
$796$	−6.23169	−	3.59787i	−0.220876	−	0.127523i
$797$	−12.8929	+	22.3311i	−0.456688	+	0.791007i	−0.998784	−	0.0493097i	$-0.984298\pi$
$797$	−12.8929	+	22.3311i	−0.456688	+	0.791007i	0.542095	+	0.840317i	$0.317631\pi$
$798$	−16.5101	−	29.8536i	−0.584453	−	1.05681i
$799$	18.0662	−	31.2916i	0.639137	−	1.10702i
$800$			2.78247i			0.0983752i
$801$	−9.72799	−	34.3385i	−0.343721	−	1.21329i
$802$	−14.4945	−	25.1052i	−0.511819	−	0.886497i
$803$	6.01202	−	10.4131i	0.212160	−	0.367471i
$804$	2.24920	−	2.97490i	0.0793231	−	0.104917i
$805$	−0.829433	+	0.603406i	−0.0292337	+	0.0212673i
$806$	7.94821	−	8.08895i	0.279964	−	0.284921i
$807$	13.2144	−	17.4780i	0.465168	−	0.615255i
$808$			35.0607i			1.23343i
$809$		−	19.7954i		−	0.695968i	−0.937500	−	0.347984i	$-0.886866\pi$
$809$		−	19.7954i		−	0.695968i	0.937500	−	0.347984i	$-0.113134\pi$
$810$	−26.4898	+	0.755885i	−0.930758	+	0.0265591i
$811$			2.30397i			0.0809035i	0.999181	+	0.0404517i	$0.0128797\pi$
$811$			2.30397i			0.0809035i	−0.999181	+	0.0404517i	$0.987120\pi$
$812$	0.0271820	+	0.257083i	0.000953902	+	0.00902183i
$813$	2.29943	−	18.4836i	0.0806444	−	0.648247i
$814$	8.01857	+	13.8886i	0.281051	+	0.486794i
$815$	21.0796	+	36.5109i	0.738385	+	1.27892i
$816$	11.6528	+	27.5744i	0.407929	+	0.965297i
$817$	−16.8187	−	9.71026i	−0.588410	−	0.339719i
$818$	−38.7012			−1.35316
$819$	−3.66394	−	28.3827i	−0.128028	−	0.991771i
$820$	8.32720			0.290799
$821$	31.5080	+	18.1912i	1.09964	+	0.634877i	0.936126	−	0.351665i	$-0.114384\pi$
$821$	31.5080	+	18.1912i	1.09964	+	0.634877i	0.163512	+	0.986541i	$0.447718\pi$
$822$	−5.72092	−	13.5376i	−0.199540	−	0.472179i
$823$	−13.9210	−	24.1119i	−0.485256	−	0.840488i	0.514600	−	0.857430i	$-0.327940\pi$
$823$	−13.9210	−	24.1119i	−0.485256	−	0.840488i	−0.999856	+	0.0169418i	$0.994607\pi$
$824$	−5.70705	−	9.88489i	−0.198814	−	0.344357i
$825$	0.662642	−	5.32654i	0.0230702	−	0.185446i
$826$	−12.8485	+	9.34717i	−0.447056	+	0.325230i
$827$		−	10.4560i		−	0.363589i	−0.983337	−	0.181795i	$-0.941809\pi$
$827$		−	10.4560i		−	0.363589i	0.983337	−	0.181795i	$-0.0581906\pi$
$828$	−0.161711	−	0.157162i	−0.00561984	−	0.00546177i
$829$		−	55.2642i		−	1.91940i	−0.281018	−	0.959702i	$-0.590672\pi$
$829$		−	55.2642i		−	1.91940i	0.281018	−	0.959702i	$-0.409328\pi$
$830$			12.3533i			0.428789i
$831$	−5.50383	+	7.27965i	−0.190926	+	0.252528i
$832$	−5.79953	−	20.9084i	−0.201063	−	0.724870i
$833$	25.6962	−	5.49529i	0.890322	−	0.190401i
$834$	11.9729	−	15.8360i	0.414588	−	0.548356i
$835$	18.3824	−	31.8393i	0.636150	−	1.10184i
$836$	−2.06847	−	3.58270i	−0.0715397	−	0.123910i
$837$	6.64028	+	8.28076i	0.229522	+	0.286225i
$838$		−	13.1235i		−	0.453342i
$839$	−12.7055	+	22.0065i	−0.438641	+	0.759749i	−0.997585	−	0.0694568i	$-0.977873\pi$
$839$	−12.7055	+	22.0065i	−0.438641	+	0.759749i	0.558944	+	0.829206i	$0.311207\pi$
$840$	−0.405065	+	21.9800i	−0.0139761	+	0.758382i
$841$	−14.4653	+	25.0546i	−0.498803	+	0.863952i
$842$	40.5496	+	23.4113i	1.39743	+	0.806808i
$843$	32.5360	−	13.7495i	1.12060	−	0.473559i
$844$	3.06328	−	5.30575i	0.105442	−	0.182631i
$845$	−21.7447	−	12.0505i	−0.748041	−	0.414550i
$846$	31.8841	+	30.9873i	1.09620	+	1.06537i
$847$	8.83253	+	12.1411i	0.303489	+	0.417172i
$848$	43.0542	−	24.8574i	1.47849	−	0.853605i
$849$	1.36315	−	0.576060i	0.0467833	−	0.0197703i
$850$	6.72215	+	3.88104i	0.230568	+	0.133118i
$851$	−0.792400	+	0.457492i	−0.0271631	+	0.0156826i
$852$	1.20637	−	0.509806i	0.0413297	−	0.0174657i
$853$			3.71099i			0.127062i	0.997980	+	0.0635310i	$0.0202362\pi$
$853$			3.71099i			0.127062i	−0.997980	+	0.0635310i	$0.979764\pi$
$854$	−43.9301	+	4.64485i	−1.50326	+	0.158943i
$855$	6.79625	−	26.8926i	0.232427	−	0.919706i
$856$	−16.3280	+	28.2808i	−0.558078	+	0.966619i
$857$	−18.2976	+	31.6923i	−0.625033	+	1.08259i	0.363502	+	0.931593i	$0.381581\pi$
$857$	−18.2976	+	31.6923i	−0.625033	+	1.08259i	−0.988535	+	0.150995i	$0.951752\pi$
$858$	−3.24590	−	21.9509i	−0.110813	−	0.749391i
$859$	32.1596	−	18.5674i	1.09727	−	0.633511i	0.161769	−	0.986829i	$-0.448280\pi$
$859$	32.1596	−	18.5674i	1.09727	−	0.633511i	0.935503	+	0.353318i	$0.114947\pi$
$860$	−1.42408	−	2.46657i	−0.0485606	−	0.0841094i
$861$	−53.8078	−	0.991614i	−1.83377	−	0.0337941i
$862$	14.4830	−	25.0852i	0.493292	−	0.854407i
$863$	−10.5667	+	6.10069i	−0.359695	+	0.207670i	−0.668947	−	0.743310i	$-0.733255\pi$
$863$	−10.5667	+	6.10069i	−0.359695	+	0.207670i	0.309252	+	0.950980i	$0.399921\pi$
$864$	−10.6416	+	1.63331i	−0.362035	+	0.0555664i
$865$	3.63145	+	6.28986i	0.123473	+	0.213862i
$866$	−8.50547	−	14.7319i	−0.289028	−	0.500610i
$867$	−4.99873	−	0.621861i	−0.169766	−	0.0211195i
$868$	−1.62048	+	1.17889i	−0.0550028	+	0.0400141i
$869$	−8.87010	+	5.12115i	−0.300898	+	0.173723i
$870$	−0.810532	+	1.07205i	−0.0274796	+	0.0363459i
$871$	5.59644	+	20.1762i	0.189628	+	0.683646i
$872$	41.3020	+	23.8457i	1.39866	+	0.807518i
$873$	2.26986	−	0.643043i	0.0768231	−	0.0217637i
$874$	1.30698	−	0.754582i	0.0442091	−	0.0255241i
$875$	18.8797	+	25.9518i	0.638251	+	0.877330i
$876$	−3.08235	+	1.30258i	−0.104143	+	0.0440102i
$877$	−49.0924			−1.65773			−0.828866	−	0.559448i	$-0.811013\pi$
$877$	−49.0924			−1.65773			−0.828866	+	0.559448i	$0.811013\pi$
$878$	−18.1519	−	31.4399i	−0.612595	−	1.06105i
$879$	50.4765	+	6.27947i	1.70253	+	0.211801i
$880$			20.3180i			0.684920i
$881$	15.0907	+	26.1379i	0.508420	+	0.880609i	0.999952	+	0.00974960i	$0.00310344\pi$
$881$	15.0907	+	26.1379i	0.508420	+	0.880609i	−0.491533	+	0.870859i	$0.663563\pi$
$882$	−1.19137	+	32.3125i	−0.0401154	+	1.08802i
$883$	15.9875			0.538023			0.269011	−	0.963137i	$-0.413303\pi$
$883$	15.9875			0.538023			0.269011	+	0.963137i	$0.413303\pi$
$884$	4.85874	+	1.25630i	0.163417	+	0.0422539i
$885$	−12.8200	−	1.59486i	−0.430940	−	0.0536105i
$886$	60.4431			2.03063
$887$	1.60978	−	2.78822i	0.0540511	−	0.0936192i	−0.837734	−	0.546079i	$-0.816120\pi$
$887$	1.60978	−	2.78822i	0.0540511	−	0.0936192i	0.891785	+	0.452459i	$0.149453\pi$
$888$	−2.42100	+	19.4608i	−0.0812433	+	0.653062i
$889$	−17.1326	+	38.5449i	−0.574609	+	1.29276i
$890$	30.3367	+	17.5149i	1.01689	+	0.587100i
$891$	20.7604	−	0.592396i	0.695500	−	0.0198460i
$892$	−3.71329	−	2.14387i	−0.124330	−	0.0717819i
$893$	−40.3026	+	23.2687i	−1.34868	+	0.778658i
$894$	27.3982	+	3.40844i	0.916332	+	0.113995i
$895$	−33.2995	+	19.2254i	−1.11308	+	0.642636i
$896$	3.73052	+	35.2826i	0.124628	+	1.17871i
$897$	1.25239	−	0.185192i	0.0418160	−	0.00618338i
$898$	20.5513	+	35.5959i	0.685806	+	1.18785i
$899$	0.538303			0.0179534
$900$	−1.04110	+	1.07124i	−0.0347035	+	0.0357079i
$901$		−	40.5344i		−	1.35040i
$902$	−41.7278			−1.38938
$903$	8.90822	+	16.1078i	0.296447	+	0.536034i
$904$	−2.69898	+	4.67476i	−0.0897666	+	0.155480i
$905$	27.9195	−	16.1193i	0.928075	−	0.535824i
$906$	6.77436	+	5.12181i	0.225063	+	0.170161i
$907$	34.3953			1.14208			0.571038	−	0.820923i	$-0.306541\pi$
$907$	34.3953			1.14208			0.571038	+	0.820923i	$0.306541\pi$
$908$	−0.205223	+	0.355457i	−0.00681056	+	0.0117962i
$909$	−29.2225	+	30.0683i	−0.969251	+	0.997303i
$910$	21.9943	+	17.4710i	0.729104	+	0.579157i
$911$			53.7798i			1.78180i	0.454196	+	0.890902i	$0.349927\pi$
$911$			53.7798i			1.78180i	−0.454196	+	0.890902i	$0.650073\pi$
$912$	4.75982	−	38.2610i	0.157613	−	1.26695i
$913$		−	9.68144i		−	0.320409i
$914$	−14.9056	+	8.60576i	−0.493034	+	0.284653i
$915$	−28.6507	−	21.6616i	−0.947163	−	0.716110i
$916$	2.42336	+	1.39913i	0.0800702	+	0.0462285i
$917$	23.5498	−	52.9824i	0.777684	−	1.74963i
$918$	−10.8972	+	27.9871i	−0.359661	+	0.923713i
$919$	−46.8145			−1.54427			−0.772134	−	0.635460i	$-0.780811\pi$
$919$	−46.8145			−1.54427			−0.772134	+	0.635460i	$0.780811\pi$
$920$	−0.972512			−0.0320628
$921$	−18.1033	+	7.65033i	−0.596523	+	0.252087i
$922$	−3.25215	+	1.87763i	−0.107104	+	0.0618364i
$923$	−1.84064	+	7.11866i	−0.0605853	+	0.234313i
$924$	−0.0722481	+	3.92039i	−0.00237679	+	0.128971i
$925$	3.03061	+	5.24917i	0.0996458	+	0.172592i
$926$	−53.5926	−	30.9417i	−1.76116	−	1.01681i
$927$	3.34451	−	13.2341i	0.109848	−	0.434665i
$928$	−0.273003	+	0.472854i	−0.00896175	+	0.0155222i
$929$	28.1976			0.925133			0.462567	−	0.886585i	$-0.346929\pi$
$929$	28.1976			0.925133			0.462567	+	0.886585i	$0.346929\pi$
$930$	−10.3383	−	1.28613i	−0.339007	−	0.0421738i
$931$	−32.2008	−	10.4184i	−1.05534	−	0.341451i
$932$	1.10095	+	0.635635i	0.0360629	+	0.0208209i
$933$	−22.1191	−	2.75170i	−0.724148	−	0.0900868i
$934$		−	8.45124i		−	0.276533i
$935$	14.3467	+	8.28304i	0.469186	+	0.270884i
$936$	13.0222	−	23.8052i	0.425642	−	0.778099i
$937$			36.5039i			1.19253i	0.802787	+	0.596266i	$0.203350\pi$
$937$			36.5039i			1.19253i	−0.802787	+	0.596266i	$0.796650\pi$
$938$	−2.48745	−	23.5258i	−0.0812180	−	0.768146i
$939$	−35.7628	−	27.0387i	−1.16707	−	0.882376i
$940$	−6.82504			−0.222608
$941$	11.6148	−	20.1174i	0.378632	−	0.655810i	−0.612231	−	0.790679i	$-0.709728\pi$
$941$	11.6148	−	20.1174i	0.378632	−	0.655810i	0.990863	+	0.134869i	$0.0430613\pi$
$942$	30.7190	−	40.6306i	1.00088	−	1.32382i
$943$		−	2.38074i		−	0.0775277i
$944$	−17.9572			−0.584457
$945$	−18.6674	+	18.5126i	−0.607251	+	0.602215i
$946$	7.13608	+	12.3601i	0.232014	+	0.401860i
$947$	1.36654	+	0.788973i	0.0444066	+	0.0256382i	0.522039	−	0.852922i	$-0.325172\pi$
$947$	1.36654	+	0.788973i	0.0444066	+	0.0256382i	−0.477632	+	0.878560i	$0.658505\pi$
$948$	2.82863	+	0.351892i	0.0918696	+	0.0114289i
$949$	4.70293	−	18.1886i	0.152664	−	0.590426i
$950$	−4.99865	−	8.65791i	−0.162178	−	0.280900i
$951$	−41.2396	−	31.1795i	−1.33729	−	1.01107i
$952$	22.7670	+	10.1196i	0.737883	+	0.327977i
$953$	32.1862	+	18.5827i	1.04261	+	0.601954i	0.920573	−	0.390571i	$-0.127722\pi$
$953$	32.1862	+	18.5827i	1.04261	+	0.601954i	0.122042	+	0.992525i	$0.461056\pi$
$954$	48.3576	+	12.2209i	1.56564	+	0.395666i
$955$	15.9191	−	9.19090i	0.515130	−	0.297411i
$956$	3.05647	−	1.76465i	0.0988533	−	0.0570730i
$957$	0.635224	−	0.840180i	0.0205339	−	0.0271592i
$958$	22.7066	+	13.1097i	0.733617	+	0.423554i
$959$	−13.3234	−	5.92205i	−0.430236	−	0.191233i
$960$	−12.0214	+	15.9001i	−0.387988	+	0.513173i
$961$	−13.4136	−	23.2331i	−0.432698	−	0.749454i
$962$	17.8728	+	17.5618i	0.576241	+	0.566214i
$963$	−37.5747	+	10.6448i	−1.21083	+	0.343023i
$964$	−2.81339	−	1.62431i	−0.0906131	−	0.0523155i
$965$	−21.4791	−	37.2028i	−0.691435	−	1.19760i
$966$	−1.43016	−	0.0263562i	−0.0460147	−	0.000847997i
$967$	20.2276			0.650475			0.325237	−	0.945632i	$-0.394556\pi$
$967$	20.2276			0.650475			0.325237	+	0.945632i	$0.394556\pi$
$968$			14.2354i			0.457544i
$969$	−25.0759	−	18.9588i	−0.805553	−	0.609044i
$970$	−1.15778	+	2.00533i	−0.0371740	+	0.0643872i
$971$	−29.7526			−0.954806			−0.477403	−	0.878685i	$-0.658422\pi$
$971$	−29.7526			−0.954806			−0.477403	+	0.878685i	$0.658422\pi$
$972$	−4.70809	−	3.35291i	−0.151012	−	0.107544i
$973$	−2.07089	−	19.5861i	−0.0663896	−	0.627901i
$974$		−	16.3779i		−	0.524781i
$975$	−1.22678	−	8.29630i	−0.0392885	−	0.265694i
$976$	−43.2370	−	24.9629i	−1.38398	−	0.799043i
$977$			30.2392i			0.967439i	0.875223	+	0.483720i	$0.160715\pi$
$977$			30.2392i			0.967439i	−0.875223	+	0.483720i	$0.839285\pi$
$978$	−7.25821	+	58.3440i	−0.232092	+	1.86563i
$979$	−23.7752	−	13.7266i	−0.759860	−	0.438705i
$980$	−3.32581	−	3.68447i	−0.106239	−	0.117696i
$981$	15.5459	+	54.8749i	0.496342	+	1.75202i
$982$	−8.73445			−0.278728
$983$	1.67455	−	2.90041i	0.0534099	−	0.0925086i	−0.838084	−	0.545541i	$-0.816324\pi$
$983$	1.67455	−	2.90041i	0.0534099	−	0.0925086i	0.891494	+	0.453032i	$0.149658\pi$
$984$	−40.7024	−	30.7734i	−1.29755	−	0.981019i
$985$	−3.79954	−	2.19367i	−0.121063	−	0.0698960i
$986$	0.761577	+	1.31909i	0.0242535	+	0.0420084i
$987$	44.1013	+	0.812734i	1.40376	+	0.0258696i
$988$	−4.61046	−	4.53024i	−0.146678	−	0.144126i
$989$	−0.705192	+	0.407143i	−0.0224238	+	0.0129464i
$990$	−14.2071	+	14.6183i	−0.451532	+	0.464600i
$991$	−16.3704			−0.520023			−0.260011	−	0.965606i	$-0.583726\pi$
$991$	−16.3704			−0.520023			−0.260011	+	0.965606i	$0.583726\pi$
$992$	−4.23246			−0.134381
$993$	−12.1542	−	28.7609i	−0.385701	−	0.912700i
$994$	3.37428	−	7.59145i	0.107026	−	0.240786i
$995$	−32.1404	−	18.5562i	−1.01892	−	0.588273i
$996$	−1.62492	+	2.14921i	−0.0514877	+	0.0681003i
$997$	−2.86694	+	1.65523i	−0.0907969	+	0.0524216i	−0.544711	−	0.838624i	$-0.683361\pi$
$997$	−2.86694	+	1.65523i	−0.0907969	+	0.0524216i	0.453914	+	0.891045i	$0.350027\pi$
$998$		−	9.06636i		−	0.286991i
$999$	−18.2966	+	14.6719i	−0.578878	+	0.464198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bf.b.185.9	yes	64
3.2	odd	2	inner	273.2.bf.b.185.24	yes	64
7.5	odd	6		273.2.r.b.68.24	yes	64
13.9	even	3		273.2.r.b.269.24	yes	64
21.5	even	6		273.2.r.b.68.9	✓	64
39.35	odd	6		273.2.r.b.269.9	yes	64
91.61	odd	6	inner	273.2.bf.b.152.24	yes	64
273.152	even	6	inner	273.2.bf.b.152.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.9	✓	64	21.5	even	6
273.2.r.b.68.24	yes	64	7.5	odd	6
273.2.r.b.269.9	yes	64	39.35	odd	6
273.2.r.b.269.24	yes	64	13.9	even	3
273.2.bf.b.152.9	yes	64	273.152	even	6	inner
273.2.bf.b.152.24	yes	64	91.61	odd	6	inner
273.2.bf.b.185.9	yes	64	1.1	even	1	trivial
273.2.bf.b.185.24	yes	64	3.2	odd	2	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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33345 - 0.769868i) q^{2} +(-0.674223 - 1.59544i) q^{3} +(0.185393 + 0.321109i) q^{4} +(0.956175 + 1.65614i) q^{5} +(-0.329235 + 2.64650i) q^{6} +(1.55646 + 2.13949i) q^{7} +2.50856i q^{8} +(-2.09085 + 2.15136i) q^{9} -2.94451i q^{10} +2.30765i q^{11} +(0.387315 - 0.512282i) q^{12} +(0.963713 + 3.47437i) q^{13} +(-0.428341 - 4.05118i) q^{14} +(1.99760 - 2.64213i) q^{15} +(2.30204 - 3.98726i) q^{16} +(-1.87695 - 3.25097i) q^{17} +(4.44430 - 1.25906i) q^{18} +4.83490i q^{19} +(-0.354536 + 0.614074i) q^{20} +(2.36402 - 3.92573i) q^{21} +(1.77659 - 3.07714i) q^{22} +(0.175563 + 0.101362i) q^{23} +(4.00225 - 1.69133i) q^{24} +(0.671459 - 1.16300i) q^{25} +(1.38974 - 5.37483i) q^{26} +(4.84206 + 1.88532i) q^{27} +(-0.398454 + 0.896441i) q^{28} +(0.228216 - 0.131761i) q^{29} +(-4.69779 + 1.98526i) q^{30} +(1.76906 + 1.02137i) q^{31} +(-1.79437 + 1.03598i) q^{32} +(3.68172 - 1.55587i) q^{33} +5.78001i q^{34} +(-2.05505 + 4.62345i) q^{35} +(-1.07845 - 0.272545i) q^{36} +(-2.25673 + 3.90878i) q^{37} +(3.72223 - 6.44709i) q^{38} +(4.89339 - 3.88004i) q^{39} +(-4.15454 + 2.39862i) q^{40} +(-5.87191 - 10.1704i) q^{41} +(-6.17460 + 3.41479i) q^{42} +(-2.00837 + 3.47860i) q^{43} +(-0.741009 + 0.427822i) q^{44} +(-5.56218 - 1.40567i) q^{45} +(-0.156070 - 0.270321i) q^{46} +(4.81266 + 8.33577i) q^{47} +(-7.91351 - 0.984471i) q^{48} +(-2.15484 + 6.66008i) q^{49} +(-1.79071 + 1.03387i) q^{50} +(-3.92124 + 5.18643i) q^{51} +(-0.936988 + 0.953580i) q^{52} +(9.35130 + 5.39898i) q^{53} +(-5.00520 - 6.24173i) q^{54} +(-3.82180 + 2.20652i) q^{55} +(-5.36704 + 3.90448i) q^{56} +(7.71378 - 3.25980i) q^{57} -0.405753 q^{58} +(-1.95014 - 3.37774i) q^{59} +(1.21875 + 0.151617i) q^{60} -10.8438i q^{61} +(-1.57263 - 2.72388i) q^{62} +(-7.85715 - 1.12484i) q^{63} -6.01791 q^{64} +(-4.83258 + 4.91815i) q^{65} +(-6.10720 - 0.759759i) q^{66} +5.80716 q^{67} +(0.695945 - 1.20541i) q^{68} +(0.0433474 - 0.348441i) q^{69} +(6.29976 - 4.58303i) q^{70} +(1.76608 + 1.01965i) q^{71} +(-5.39682 - 5.24502i) q^{72} +(-4.51243 - 2.60525i) q^{73} +(6.01849 - 3.47477i) q^{74} +(-2.30821 - 0.287150i) q^{75} +(-1.55253 + 0.896354i) q^{76} +(-4.93720 + 3.59178i) q^{77} +(-9.51221 + 1.40658i) q^{78} +(2.21921 + 3.84378i) q^{79} +8.80463 q^{80} +(-0.256710 - 8.99634i) q^{81} +18.0824i q^{82} -4.19536 q^{83} +(1.69886 + 0.0313080i) q^{84} +(3.58938 - 6.21699i) q^{85} +(5.35612 - 3.09236i) q^{86} +(-0.364084 - 0.275269i) q^{87} -5.78888 q^{88} +(-5.94831 + 10.3028i) q^{89} +(6.33471 + 6.15653i) q^{90} +(-5.93340 + 7.46959i) q^{91} +0.0751668i q^{92} +(0.436788 - 3.51105i) q^{93} -14.8204i q^{94} +(-8.00728 + 4.62301i) q^{95} +(2.86265 + 2.16433i) q^{96} +(-0.681039 - 0.393198i) q^{97} +(8.00076 - 7.22194i) q^{98} +(-4.96459 - 4.82495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Introduction

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