LMFDB - Embedded newform 273.2.bf.b.185.24

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			185.24
Character	$\chi$	$=$	273.185
Dual form			273.2.bf.b.152.24

$q$-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} +(2.12732 - 1.60838i) 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} +(0.637306 - 0.0792833i) q^{12} +(0.963713 + 3.47437i) q^{13} +(0.428341 + 4.05118i) q^{14} +(-3.28695 + 0.408909i) q^{15} +(2.30204 - 3.98726i) q^{16} +(1.87695 + 3.25097i) q^{17} +(-1.13178 - 4.47841i) q^{18} +4.83490i q^{19} +(0.354536 - 0.614074i) q^{20} +(4.46283 - 1.04075i) 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} +(0.303195 - 1.07024i) q^{36} +(-2.25673 + 3.90878i) q^{37} +(-3.72223 + 6.44709i) q^{38} +(6.19290 + 0.804955i) q^{39} +(-4.15454 + 2.39862i) q^{40} +(5.87191 + 10.1704i) q^{41} +(6.75220 + 2.04800i) q^{42} +(-2.00837 + 3.47860i) q^{43} +(0.741009 - 0.427822i) q^{44} +(-1.56375 + 5.51982i) q^{45} +(-0.156070 - 0.270321i) q^{46} +(-4.81266 - 8.33577i) q^{47} +(-4.80933 - 6.36107i) q^{48} +(-2.15484 + 6.66008i) q^{49} +(1.79071 - 1.03387i) q^{50} +(6.45220 - 0.802678i) q^{51} +(-0.936988 + 0.953580i) q^{52} +(-9.35130 - 5.39898i) q^{53} +(-7.90810 - 1.21376i) 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} +(-0.740681 - 0.979662i) q^{60} -10.8438i q^{61} +(1.57263 + 2.72388i) q^{62} +(1.34849 - 7.82187i) q^{63} -6.01791 q^{64} +(4.83258 - 4.91815i) q^{65} +(-3.71157 - 4.90911i) q^{66} +5.80716 q^{67} +(-0.695945 + 1.20541i) q^{68} +(-0.280085 + 0.211760i) 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} +(-1.40278 - 1.85539i) q^{75} +(-1.55253 + 0.896354i) q^{76} +(4.93720 - 3.59178i) q^{77} +(7.63822 + 5.84108i) 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} +(1.16157 + 1.24011i) q^{84} +(3.58938 - 6.21699i) q^{85} +(-5.35612 + 3.09236i) q^{86} +(0.0563475 + 0.452940i) 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} +(2.82226 - 2.13379i) q^{93} -14.8204i q^{94} +(8.00728 - 4.62301i) q^{95} +(-0.443038 - 3.56129i) 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	0.890866	−	0.454267i	$-0.150099\pi$
$2$	1.33345	+	0.769868i	0.942892	+	0.544379i	0.0520260	+	0.998646i	$0.483432\pi$
$3$	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	0.569046	−	0.822306i	$-0.307313\pi$
$5$	−0.956175	−	1.65614i	−0.427614	−	0.740650i	−0.996661	+	0.0816556i	$0.973979\pi$
$6$	2.12732	−	1.60838i	0.868474	−	0.656616i
$7$	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	$-0.886898\pi$
$11$		−	2.30765i		−	0.695783i	0.937535	−	0.347892i	$-0.113102\pi$
$12$	0.637306	−	0.0792833i	0.183974	−	0.0228871i
$13$	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
$15$	−3.28695	+	0.408909i	−0.848687	+	0.105580i
$16$	2.30204	−	3.98726i	0.575511	−	0.996814i
$17$	1.87695	+	3.25097i	0.455227	+	0.788476i	0.998701	−	0.0509499i	$-0.0162249\pi$
$17$	1.87695	+	3.25097i	0.455227	+	0.788476i	−0.543474	+	0.839426i	$0.682892\pi$
$18$	−1.13178	−	4.47841i	−0.266763	−	1.05557i
$19$			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
$21$	4.46283	−	1.04075i	0.973869	−	0.227110i
$22$	1.77659	−	3.07714i	0.378770	−	0.656048i
$23$	−0.175563	−	0.101362i	−0.0366075	−	0.0211353i	0.481585	−	0.876400i	$-0.340061\pi$
$23$	−0.175563	−	0.101362i	−0.0366075	−	0.0211353i	−0.518192	+	0.855264i	$0.673395\pi$
$24$	−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	−0.521040	−	0.853532i	$-0.674456\pi$
$29$	−0.228216	+	0.131761i	−0.0423786	+	0.0244673i	0.478661	+	0.878000i	$0.341122\pi$
$30$	−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
$36$	0.303195	−	1.07024i	0.0505324	−	0.178373i
$37$	−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
$39$	6.19290	+	0.804955i	0.991658	+	0.128896i
$40$	−4.15454	+	2.39862i	−0.656890	+	0.379255i
$41$	5.87191	+	10.1704i	0.917038	+	1.58836i	0.803889	+	0.594779i	$0.202760\pi$
$41$	5.87191	+	10.1704i	0.917038	+	1.58836i	0.113149	+	0.993578i	$0.463906\pi$
$42$	6.75220	+	2.04800i	1.04189	+	0.316014i
$43$	−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
$45$	−1.56375	+	5.51982i	−0.233110	+	0.822847i
$46$	−0.156070	−	0.270321i	−0.0230113	−	0.0398567i
$47$	−4.81266	−	8.33577i	−0.701999	−	1.21590i	−0.967764	−	0.251860i	$-0.918958\pi$
$47$	−4.81266	−	8.33577i	−0.701999	−	1.21590i	0.265765	−	0.964038i	$-0.414375\pi$
$48$	−4.80933	−	6.36107i	−0.694168	−	0.918141i
$49$	−2.15484	+	6.66008i	−0.307835	+	0.951440i
$50$	1.79071	−	1.03387i	0.253245	−	0.146211i
$51$	6.45220	−	0.802678i	0.903489	−	0.112397i
$52$	−0.936988	+	0.953580i	−0.129937	+	0.132238i
$53$	−9.35130	−	5.39898i	−1.28450	−	0.741606i	−0.306832	−	0.951764i	$-0.599269\pi$
$53$	−9.35130	−	5.39898i	−1.28450	−	0.741606i	−0.977668	+	0.210157i	$0.932602\pi$
$54$	−7.90810	−	1.21376i	−1.07616	−	0.165172i
$55$	−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	0.964592	−	0.263745i	$-0.0849578\pi$
$59$	1.95014	+	3.37774i	0.253886	+	0.439744i	−0.710706	+	0.703489i	$0.751624\pi$
$60$	−0.740681	−	0.979662i	−0.0956215	−	0.126474i
$61$		−	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
$63$	1.34849	−	7.82187i	0.169894	−	0.985462i
$64$	−6.01791			−0.752238
$65$	4.83258	−	4.91815i	0.599408	−	0.610022i
$66$	−3.71157	−	4.90911i	−0.456863	−	0.604270i
$67$	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
$69$	−0.280085	+	0.211760i	−0.0337183	+	0.0254929i
$70$	6.29976	−	4.58303i	0.752965	−	0.547776i
$71$	−1.76608	−	1.01965i	−0.209595	−	0.121010i	0.391528	−	0.920166i	$-0.371947\pi$
$71$	−1.76608	−	1.01965i	−0.209595	−	0.121010i	−0.601123	+	0.799156i	$0.705280\pi$
$72$	−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
$75$	−1.40278	−	1.85539i	−0.161979	−	0.214242i
$76$	−1.55253	+	0.896354i	−0.178088	+	0.102819i
$77$	4.93720	−	3.59178i	0.562646	−	0.409321i
$78$	7.63822	+	5.84108i	0.864858	+	0.661373i
$79$	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	$-0.426045\pi$
$83$	4.19536			0.460501			0.230250	+	0.973131i	$0.426045\pi$
$84$	1.16157	+	1.24011i	0.126738	+	0.135307i
$85$	3.58938	−	6.21699i	0.389323	−	0.674327i
$86$	−5.35612	+	3.09236i	−0.577565	+	0.333457i
$87$	0.0563475	+	0.452940i	0.00604109	+	0.0485603i
$88$	−5.78888			−0.617097
$89$	5.94831	−	10.3028i	0.630520	−	1.09209i	−0.356925	−	0.934133i	$-0.616175\pi$
$89$	5.94831	−	10.3028i	0.630520	−	1.09209i	0.987446	−	0.157960i	$-0.0504917\pi$
$90$	−6.33471	+	6.15653i	−0.667737	+	0.648955i
$91$	−5.93340	+	7.46959i	−0.621990	+	0.783025i
$92$		−	0.0751668i		−	0.00783668i
$93$	2.82226	−	2.13379i	0.292655	−	0.221264i
$94$		−	14.8204i		−	1.52861i
$95$	8.00728	−	4.62301i	0.821530	−	0.474311i
$96$	−0.443038	−	3.56129i	−0.0452173	−	0.363472i
$97$	−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	$-0.744752\pi$
$101$	−13.9764			−1.39070			−0.695352	+	0.718669i	$0.744752\pi$
$102$	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
$105$	−5.99087	−	6.39595i	−0.584650	−	0.624181i
$106$	−8.31299	−	14.3985i	−0.807429	−	1.39851i
$107$	−11.2737	−	6.50890i	−1.08987	−	0.629239i	−0.156331	−	0.987705i	$-0.549967\pi$
$107$	−11.2737	−	6.50890i	−1.08987	−	0.629239i	−0.933543	+	0.358466i	$0.883300\pi$
$108$	−1.50308	−	1.20531i	−0.144634	−	0.115981i
$109$	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
$111$	4.71468	+	6.23587i	0.447497	+	0.591882i
$112$	12.1138	−	1.28082i	1.14464	−	0.121026i
$113$	−1.86352	−	1.07591i	−0.175306	−	0.101213i	0.409780	−	0.912185i	$-0.365606\pi$
$113$	−1.86352	−	1.07591i	−0.175306	−	0.101213i	−0.585085	+	0.810972i	$0.698939\pi$
$114$	7.77633	+	10.2854i	0.728320	+	0.963313i
$115$			0.387678i			0.0361511i
$116$	−0.0846191	−	0.0488549i	−0.00785669	−	0.00453606i
$117$	5.45965	−	9.33768i	0.504745	−	0.863269i
$118$			6.00539i			0.552841i
$119$	−4.03402	+	9.07573i	−0.369798	+	0.831971i
$120$	1.02577	+	8.24551i	0.0936398	+	0.752709i
$121$	5.67474			0.515886
$122$	8.34829	−	14.4597i	0.755819	−	1.30912i
$123$	20.1853	−	2.51113i	1.82005	−	0.226421i
$124$			0.757415i			0.0680179i
$125$	−12.1299			−1.08493
$126$	7.81994	−	9.39191i	0.696656	−	0.836698i
$127$	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
$129$	4.19580	+	5.54958i	0.369420	+	0.488613i
$130$	10.2303	−	2.83766i	0.897260	−	0.248880i
$131$	10.9573	+	18.9785i	0.957341	+	1.65816i	0.728918	+	0.684601i	$0.240024\pi$
$131$	10.9573	+	18.9785i	0.957341	+	1.65816i	0.228423	+	0.973562i	$0.426643\pi$
$132$	−0.182958	−	1.47068i	−0.0159245	−	0.128006i
$133$	−10.3442	+	7.52534i	−0.896958	+	0.652530i
$134$	7.74356	+	4.47075i	0.668942	+	0.386214i
$135$	7.75222	+	6.21645i	0.667205	+	0.535027i
$136$	8.15525	−	4.70844i	0.699307	−	0.403745i
$137$	4.77251	−	2.75541i	0.407743	−	0.235411i	−0.282076	−	0.959392i	$-0.591023\pi$
$137$	4.77251	−	2.75541i	0.407743	−	0.235411i	0.689820	+	0.723981i	$0.257690\pi$
$138$	−0.536507	+	0.0667435i	−0.0456705	+	0.00568158i
$139$	−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
$141$	−16.5440	+	2.05814i	−1.39326	+	0.173327i
$142$	−1.56998	−	2.71929i	−0.131750	−	0.228198i
$143$	8.01764	−	2.22391i	0.670469	−	0.185973i
$144$	−13.3913	+	3.38422i	−1.11594	+	0.282018i
$145$	0.436429	+	0.251972i	0.0362434	+	0.0209252i
$146$	−4.01140	−	6.94795i	−0.331986	−	0.575016i
$147$	9.17290	+	7.92829i	0.756568	+	0.653915i
$148$	−1.67353			−0.137563
$149$			10.3526i			0.848119i	0.905634	+	0.424059i	$0.139395\pi$
$149$			10.3526i			0.848119i	−0.905634	+	0.424059i	$0.860605\pi$
$150$	−0.442135	−	3.55403i	−0.0361002	−	0.290185i
$151$	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
$153$	3.06960	−	10.8353i	0.248162	−	0.875980i
$154$	9.34870	−	0.988462i	0.753340	−	0.0796526i
$155$		−	3.90642i		−	0.313771i
$156$	0.889640	+	2.13783i	0.0712282	+	0.171164i
$157$	−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
$159$	−14.9186	+	11.2793i	−1.18312	+	0.894508i
$160$	−3.43146	−	1.98116i	−0.271281	−	0.156624i
$161$	−0.0563958	−	0.533382i	−0.00444461	−	0.0420364i
$162$	−7.26830	+	11.7985i	−0.571052	+	0.926980i
$163$	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
$165$	0.943620	+	7.58514i	0.0734607	+	0.590502i
$166$	5.59431	+	3.22987i	0.434202	+	0.250687i
$167$	9.61248	+	16.6493i	0.743836	+	1.28836i	0.950736	+	0.310000i	$0.100329\pi$
$167$	9.61248	+	16.6493i	0.743836	+	1.28836i	−0.206900	+	0.978362i	$0.566338\pi$
$168$	−2.61078	−	11.1953i	−0.201426	−	0.863734i
$169$	−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	$-0.546117\pi$
$173$	−3.79789			−0.288748			−0.144374	+	0.989523i	$0.546117\pi$
$174$	−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
$177$	6.70380	−	0.833978i	0.503888	−	0.0626856i
$178$	15.8636	−	9.15883i	1.18902	−	0.686483i
$179$		−	20.1066i		−	1.50284i	−0.659825	−	0.751420i	$-0.729369\pi$
$179$		−	20.1066i		−	1.50284i	0.659825	−	0.751420i	$-0.270631\pi$
$180$	−2.06237	+	0.521201i	−0.153720	+	0.0388480i
$181$		−	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
$186$	5.40609	−	0.672538i	0.396394	−	0.0493129i
$187$	7.50211	−	4.33134i	0.548608	−	0.316739i
$188$	1.78446	−	3.09078i	0.130145	−	0.225418i
$189$	−11.5701	−	7.42511i	−0.841603	−	0.540097i
$190$	14.2364			1.03282
$191$			9.61215i			0.695511i	0.937585	+	0.347756i	$0.113056\pi$
$191$			9.61215i			0.695511i	−0.937585	+	0.347756i	$0.886944\pi$
$192$	−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
$195$	−4.58838	−	11.0260i	−0.328581	−	0.789589i
$196$	−2.53811	+	0.542789i	−0.181293	+	0.0387706i
$197$	1.98684	−	1.14711i	0.141557	−	0.0817279i	−0.427549	−	0.903992i	$-0.640623\pi$
$197$	1.98684	−	1.14711i	0.141557	−	0.0817279i	0.569106	+	0.822264i	$0.307290\pi$
$198$	−10.3346	+	2.61175i	−0.734449	+	0.185609i
$199$	−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
$204$	1.45394	+	1.92305i	0.101796	+	0.134641i
$205$	11.2291	−	19.4495i	0.784278	−	1.35841i
$206$	−7.00589			−0.488123
$207$	0.149011	+	0.589632i	0.0103570	+	0.0409822i
$208$	16.0717	+	4.15559i	1.11437	+	0.288138i
$209$	11.1573			0.771764
$210$	−3.06450	−	13.1409i	−0.211470	−	0.906805i
$211$	−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
$213$	−2.81751	+	2.13020i	−0.193053	+	0.145959i
$214$	−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
$219$	−7.19890	+	5.44279i	−0.486457	+	0.367789i
$220$	−1.41707	−	0.818145i	−0.0955387	−	0.0551593i
$221$	−9.48624	+	9.65421i	−0.638113	+	0.649413i
$222$	1.48599	+	11.9449i	0.0997331	+	0.801689i
$223$	−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
$225$	−3.90595	+	0.987107i	−0.260397	+	0.0658072i
$226$	−1.65661	−	2.86933i	−0.110196	−	0.190865i
$227$	−0.553482	−	0.958659i	−0.0367359	−	0.0636284i	0.847073	−	0.531477i	$-0.178363\pi$
$227$	−0.553482	−	0.958659i	−0.0367359	−	0.0636284i	−0.883809	+	0.467848i	$0.845029\pi$
$228$	0.383327	+	3.08131i	0.0253864	+	0.204065i
$229$	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
$231$	−2.40169	−	10.2987i	−0.158019	−	0.677602i
$232$	0.330529	+	0.572493i	0.0217003	+	0.0375860i
$233$	−2.96925	+	1.71430i	−0.194522	+	0.112307i	−0.594098	−	0.804393i	$-0.702491\pi$
$233$	−2.96925	+	1.71430i	−0.194522	+	0.112307i	0.399576	+	0.916700i	$0.369157\pi$
$234$	14.4689	−	8.24812i	0.945865	−	0.539196i
$235$	−9.20349	+	15.9409i	−0.600370	+	1.03987i
$236$	−0.723082	+	1.25242i	−0.0470686	+	0.0815253i
$237$	7.62875	−	0.949045i	0.495540	−	0.0616471i
$238$	−12.3663	+	8.99637i	−0.801586	+	0.583148i
$239$			9.51846i			0.615698i	0.951435	+	0.307849i	$0.0996092\pi$
$239$			9.51846i			0.615698i	−0.951435	+	0.307849i	$0.900391\pi$
$240$	−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	$0.376596\pi$
$251$	−9.70748	+	16.8139i	−0.612731	+	1.06128i	−0.990778	+	0.135495i	$0.956738\pi$
$252$	2.76168	−	1.01710i	0.173969	−	0.0640715i
$253$	−0.233907	+	0.405139i	−0.0147056	+	0.0254709i
$254$			24.5479i			1.54027i
$255$	−7.49878	−	9.91827i	−0.469592	−	0.621106i
$256$	−4.30595	−	7.45812i	−0.269122	−	0.466132i
$257$	−7.58876	+	13.1441i	−0.473374	+	0.819907i	−0.999535	−	0.0304772i	$-0.990297\pi$
$257$	−7.58876	+	13.1441i	−0.473374	+	0.819907i	0.526162	+	0.850384i	$0.323631\pi$
$258$	1.32245	+	10.6303i	0.0823321	+	0.661813i
$259$	−11.8753	+	1.25561i	−0.737897	+	0.0780197i
$260$	2.47519	+	0.639998i	0.153505	+	0.0396910i
$261$	0.760629	+	0.215484i	0.0470818	+	0.0133381i
$262$			33.7426i			2.08462i
$263$			1.74892i			0.107843i	0.998545	+	0.0539214i	$0.0171720\pi$
$263$			1.74892i			0.107843i	−0.998545	+	0.0539214i	$0.982828\pi$
$264$	−3.90300	+	9.23581i	−0.240213	+	0.568425i
$265$			20.6495i			1.26849i
$266$	−19.5870	+	2.07099i	−1.20096	+	0.126980i
$267$	−12.4270	−	16.4365i	−0.760518	−	1.00590i
$268$	1.07661	+	1.86473i	0.0657641	+	0.113907i
$269$	−6.32521	−	10.9556i	−0.385655	−	0.667974i	0.606205	−	0.795309i	$-0.292691\pi$
$269$	−6.32521	−	10.9556i	−0.385655	−	0.667974i	−0.991860	+	0.127334i	$0.959358\pi$
$270$	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
$273$	7.91683	+	14.5025i	0.479148	+	0.877734i
$274$	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
$279$	−1.50150	−	5.94140i	−0.0898927	−	0.355702i
$280$	−11.5982	−	5.15522i	−0.693126	−	0.308084i
$281$		−	20.3932i		−	1.21655i	−0.793725	−	0.608277i	$-0.791861\pi$
$281$		−	20.3932i		−	1.21655i	0.793725	−	0.608277i	$-0.208139\pi$
$282$	−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
$285$	−1.97703	−	15.8921i	−0.117109	−	0.941365i
$286$	12.4032	+	3.20705i	0.733419	+	0.189637i
$287$	−12.6202	+	28.3928i	−0.744945	+	1.67598i
$288$	−5.98052	−	1.69426i	−0.352406	−	0.0998353i
$289$	1.45413	−	2.51863i	0.0855373	−	0.148155i
$290$	0.387971	+	0.671985i	0.0227824	+	0.0394603i
$291$	−1.08649	+	0.821453i	−0.0636915	+	0.0481544i
$292$		−	1.93198i		−	0.113061i
$293$	14.6836	−	25.4328i	0.857828	−	1.48580i	−0.0161693	−	0.999869i	$-0.505147\pi$
$293$	14.6836	−	25.4328i	0.857828	−	1.48580i	0.873997	−	0.485932i	$-0.161520\pi$
$294$	6.12787	+	17.6339i	0.357385	+	1.02843i
$295$	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
$309$	0.972918	+	7.82065i	0.0553474	+	0.444901i
$310$	3.00743	−	5.20901i	0.170810	−	0.295852i
$311$	−6.43447	+	11.1448i	−0.364865	+	0.631965i	−0.988755	−	0.149548i	$-0.952218\pi$
$311$	−6.43447	+	11.1448i	−0.364865	+	0.631965i	0.623889	+	0.781513i	$0.285552\pi$
$312$	2.01928	−	15.5353i	0.114319	−	0.879511i
$313$	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
$315$	−14.2435	+	5.24578i	−0.802532	+	0.295566i
$316$	−0.822849	+	1.42522i	−0.0462889	+	0.0801747i
$317$	−25.8499	+	14.9244i	−1.45187	+	0.838240i	−0.998588	−	0.0531246i	$-0.983082\pi$
$317$	−25.8499	+	14.9244i	−1.45187	+	0.838240i	−0.453287	+	0.891365i	$0.649749\pi$
$318$	−28.5768	+	3.55506i	−1.60251	+	0.199358i
$319$	0.304057	+	0.526643i	0.0170240	+	0.0294863i
$320$	5.75417	+	9.96652i	0.321668	+	0.557145i
$321$	−17.9855	+	13.5981i	−1.00386	+	0.758973i
$322$	0.335432	−	0.754655i	0.0186929	−	0.0420553i
$323$	−15.7181	+	9.07485i	−0.874579	+	0.504938i
$324$	−2.93640	+	1.58542i	−0.163133	+	0.0880791i
$325$	4.68779	+	1.21210i	0.260032	+	0.0672351i
$326$	29.3969	+	16.9723i	1.62814	+	0.940008i
$327$	−19.8590	−	26.2665i	−1.09821	−	1.45254i
$328$	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
$333$	13.1277	−	3.31761i	0.719393	−	0.181804i
$334$			29.6014i			1.61971i
$335$	−5.55266	−	9.61749i	−0.303374	−	0.525460i
$336$	6.12390	−	20.1903i	0.334086	−	1.10147i
$337$	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
$339$	−2.97297	+	2.24774i	−0.161470	+	0.122080i
$340$	2.66178			0.144355
$341$	2.35696	−	4.08237i	0.127636	−	0.221073i
$342$	21.6526	−	5.47203i	1.17084	−	0.295893i
$343$	−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	−0.939554	−	0.342402i	$-0.888759\pi$
$347$	−20.7292	+	11.9680i	−1.11280	+	0.642476i	−0.173248	+	0.984878i	$0.555426\pi$
$348$	−0.134997	+	0.102066i	−0.00723660	+	0.00547129i
$349$	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
$351$	−11.2167	−	15.0062i	−0.598702	−	0.800972i
$352$	−2.39068	−	4.14078i	−0.127424	−	0.220704i
$353$	−9.49437			−0.505334			−0.252667	−	0.967553i	$-0.581308\pi$
$353$	−9.49437			−0.505334			−0.252667	+	0.967553i	$0.581308\pi$
$354$	9.58123	+	4.04897i	0.509237	+	0.215200i
$355$			3.89984i			0.206982i
$356$	4.41110			0.233788
$357$	11.7599	+	12.5551i	0.622402	+	0.664486i
$358$	15.4794	−	26.8112i	0.818114	−	1.41701i
$359$	31.0183	−	17.9084i	1.63708	−	0.945171i	0.655255	−	0.755408i	$-0.272561\pi$
$359$	31.0183	−	17.9084i	1.63708	−	0.945171i	0.981830	−	0.189764i	$-0.0607722\pi$
$360$	13.8468	+	3.92275i	0.729791	+	0.206747i
$361$	−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
$366$	−17.4409	−	23.0682i	−0.911651	−	1.20580i
$367$			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
$369$	9.60303	−	33.8975i	0.499914	−	1.76463i
$370$	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
$378$	−9.71183	−	18.8085i	−0.499523	−	0.967404i
$379$	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
$381$	27.4027	−	3.40900i	1.40388	−	0.174648i
$382$	−7.40009	+	12.8173i	−0.378621	+	0.655792i
$383$	−30.7820			−1.57289			−0.786443	−	0.617663i	$-0.788080\pi$
$383$	−30.7820			−1.57289			−0.786443	+	0.617663i	$0.788080\pi$
$384$	−18.5273	+	14.0077i	−0.945467	+	0.714828i
$385$	−10.6693	−	4.74235i	−0.543759	−	0.241692i
$386$	−29.9540	−	17.2939i	−1.52462	−	0.880238i
$387$	11.6829	−	2.95249i	0.593876	−	0.150084i
$388$		−	0.291584i		−	0.0148029i
$389$	6.92484	+	3.99806i	0.351103	+	0.202710i	0.665171	−	0.746691i	$-0.268359\pi$
$389$	6.92484	+	3.99806i	0.351103	+	0.202710i	−0.314068	+	0.949401i	$0.601692\pi$
$390$	2.37020	−	18.2351i	0.120020	−	0.923369i
$391$		−	0.761002i		−	0.0384855i
$392$	16.7072	+	5.40555i	0.843841	+	0.273022i
$393$	37.6667	−	4.68588i	1.90004	−	0.236372i
$394$	3.53248			0.177964
$395$	4.24390	−	7.35065i	0.213534	−	0.369851i
$396$	−2.46974	−	0.699668i	−0.124109	−	0.0351596i
$397$			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
$399$	5.03191	+	21.5773i	0.251911	+	1.08022i
$400$	−3.09146	−	5.35456i	−0.154573	−	0.267728i
$401$	−16.3049	−	9.41364i	−0.814228	−	0.470095i	0.0341939	−	0.999415i	$-0.489114\pi$
$401$	−16.3049	−	9.41364i	−0.814228	−	0.470095i	−0.848422	+	0.529320i	$0.822447\pi$
$402$	12.3537	−	9.34010i	0.616146	−	0.465842i
$403$	−1.84374	+	7.13067i	−0.0918433	+	0.355204i
$404$	−2.59112	−	4.48796i	−0.128913	−	0.223284i
$405$	15.1447	−	8.17693i	0.752546	−	0.406315i
$406$	−0.631539	−	0.868104i	−0.0313428	−	0.0430833i
$407$	9.02010	+	5.20776i	0.447110	+	0.258139i
$408$	−2.01357	−	16.1857i	−0.0996864	−	0.801313i
$409$	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
$411$	−1.17835	−	9.47201i	−0.0581239	−	0.467220i
$412$	−1.46107	−	0.843547i	−0.0719816	−	0.0415586i
$413$	−4.19132	+	9.42962i	−0.206241	+	0.464001i
$414$	−0.255240	+	0.900963i	−0.0125444	+	0.0442799i
$415$	−4.01150	−	6.94812i	−0.196917	−	0.341070i
$416$	5.32864	+	5.23592i	0.261258	+	0.256712i
$417$	−10.2849	+	7.77596i	−0.503653	+	0.380791i
$418$	14.8777	+	8.58962i	0.727690	+	0.420132i
$419$	−4.26159	−	7.38130i	−0.208193	−	0.360600i	0.742953	−	0.669344i	$-0.233425\pi$
$419$	−4.26159	−	7.38130i	−0.208193	−	0.360600i	−0.951145	+	0.308744i	$0.900091\pi$
$420$	0.943136	−	3.10949i	0.0460203	−	0.151728i
$421$	−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
$423$	−7.87072	+	27.7826i	−0.382687	+	1.35084i
$424$	−13.5437	+	23.4583i	−0.657738	+	1.13924i
$425$	5.04117			0.244533
$426$	−5.39698	+	0.671405i	−0.261485	+	0.0325297i
$427$	23.2002	−	16.8780i	1.12274	−	0.816783i
$428$		−	4.82681i		−	0.233312i
$429$	1.85756	−	14.2911i	0.0896837	−	0.689979i
$430$	10.2428	+	5.91367i	0.493950	+	0.285182i
$431$		−	18.8123i		−	0.906156i	−0.891471	−	0.453078i	$-0.850326\pi$
$431$		−	18.8123i		−	0.906156i	0.891471	−	0.453078i	$-0.149674\pi$
$432$	−3.62937	+	23.6466i	−0.174618	+	1.13770i
$433$	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
$435$	0.696256	−	0.526410i	0.0333829	−	0.0252394i
$436$	7.04918			0.337595
$437$	0.490073	−	0.848831i	0.0234434	−	0.0406051i
$438$	−13.7896	+	1.71548i	−0.658893	+	0.0819688i
$439$	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
$441$	18.8337	−	9.28937i	0.896842	−	0.442351i
$442$	−20.0819	+	5.57027i	−0.955198	+	0.264951i
$443$	33.9963	−	19.6278i	1.61521	−	0.932543i	0.627076	−	0.778958i	$-0.284252\pi$
$443$	33.9963	−	19.6278i	1.61521	−	0.932543i	0.988136	−	0.153584i	$-0.0490817\pi$
$444$	−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	0.933846	−	0.357674i	$-0.116430\pi$
$449$	23.1182	+	13.3473i	1.09101	+	0.629898i	0.157168	+	0.987572i	$0.449763\pi$
$450$	−5.96833	−	1.69081i	−0.281350	−	0.0797055i
$451$	23.4699	−	13.5503i	1.10515	−	0.638060i
$452$		−	0.797861i		−	0.0375282i
$453$	−3.32642	−	4.39969i	−0.156289	−	0.206716i
$454$		−	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
$459$	−15.2174	−	12.2027i	−0.710289	−	0.569575i
$460$	−0.124487	+	0.0718726i	−0.00580423	+	0.00335108i
$461$	−1.21945	+	2.11215i	−0.0567954	+	0.0983725i	−0.893025	−	0.450007i	$-0.851422\pi$
$461$	−1.21945	+	2.11215i	−0.0567954	+	0.0983725i	0.836230	+	0.548379i	$0.184755\pi$
$462$	4.72608	−	15.5817i	0.219877	−	0.724927i
$463$	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	0.795516	−	0.605932i	$-0.207200\pi$
$467$	−2.74438	−	4.75341i	−0.126995	−	0.219961i	−0.922511	+	0.385971i	$0.873866\pi$
$468$	4.01060	+	0.0220092i	0.185390	+	0.00101738i
$469$	9.03863	+	12.4244i	0.417365	+	0.573704i
$470$	−24.5448	+	14.1709i	−1.13217	+	0.653657i
$471$	−26.3880	+	19.9509i	−1.21590	+	0.919287i
$472$	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
$477$	7.93700	+	31.4065i	0.363410	+	1.43800i
$478$	−7.32796	+	12.6924i	−0.335173	+	0.580537i
$479$	17.0285			0.778050			0.389025	−	0.921227i	$-0.372812\pi$
$479$	17.0285			0.778050			0.389025	+	0.921227i	$0.372812\pi$
$480$	−5.47438	+	4.13895i	−0.249870	+	0.188916i
$481$	−15.7554	−	4.07380i	−0.718384	−	0.185749i
$482$	−13.4903			−0.614468
$483$	−0.889001	−	0.269642i	−0.0404510	−	0.0122691i
$484$	1.05206	+	1.82221i	0.0478207	+	0.0828279i
$485$			1.50386i			0.0682870i
$486$	13.9234	+	19.5510i	0.631578	+	0.886850i
$487$	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	−0.606740	−	0.794900i	$-0.707523\pi$
$491$	−4.91270	+	2.83635i	−0.221707	+	0.128003i	0.385033	+	0.922903i	$0.374190\pi$
$492$	4.54855	+	6.01615i	0.205065	+	0.271229i
$493$	−0.856699	−	0.494615i	−0.0385838	−	0.0222764i
$494$	−25.9868	−	6.71927i	−1.16920	−	0.302314i
$495$	12.7378	+	3.60858i	0.572523	+	0.162194i
$496$	8.14490	−	4.70246i	0.365717	−	0.211147i
$497$	−0.567313	−	5.36555i	−0.0254475	−	0.240678i
$498$	8.92487	−	6.74772i	0.399933	−	0.302372i
$499$	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
$501$	33.0439	−	4.11079i	1.47629	−	0.183656i
$502$	−25.8889	+	14.9470i	−1.15548	+	0.667115i
$503$	−7.14545	+	12.3763i	−0.318600	+	0.551831i	−0.980196	−	0.198029i	$-0.936546\pi$
$503$	−7.14545	+	12.3763i	−0.318600	+	0.551831i	0.661596	+	0.749860i	$0.269879\pi$
$504$	−19.6216	−	3.38277i	−0.874016	−	0.150680i
$505$	13.3639	+	23.1469i	0.594685	+	1.03003i
$506$	−0.623807	+	0.360155i	−0.0277316	+	0.0160109i
$507$	3.17147	+	22.2922i	0.140850	+	0.990031i
$508$	−2.95570	+	5.11942i	−0.131138	+	0.227138i
$509$	10.6611	−	18.4656i	0.472545	−	0.818472i	−0.526961	−	0.849889i	$-0.676669\pi$
$509$	10.6611	−	18.4656i	0.472545	−	0.818472i	0.999506	+	0.0314171i	$0.0100020\pi$
$510$	−2.36350	−	18.9986i	−0.104657	−	0.841272i
$511$	−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	−0.894445	−	0.447179i	$-0.852429\pi$
$521$	−1.36848	+	2.37027i	−0.0599540	+	0.103843i	0.834491	+	0.551022i	$0.185762\pi$
$522$	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
$525$	1.78621	−	5.88909i	0.0779568	−	0.257021i
$526$	−1.34643	+	2.33209i	−0.0587073	+	0.101684i
$527$			7.66820i			0.334032i
$528$	−14.6791	+	11.0983i	−0.638827	+	0.482990i
$529$	−11.4795	−	19.8830i	−0.499107	−	0.864478i
$530$	−15.8974	+	27.5350i	−0.690537	+	1.19605i
$531$	3.18929	−	11.2578i	0.138403	−	0.488546i
$532$	−4.33420	−	1.92648i	−0.187911	−	0.0835237i
$533$	−29.6771	+	30.2026i	−1.28546	+	1.30822i
$534$	−3.91678	−	31.4844i	−0.169496	−	1.36246i
$535$			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
$540$	−0.558956	+	3.64180i	−0.0240536	+	0.156718i
$541$	−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
$546$	−0.608340	+	25.4333i	−0.0260345	+	1.08845i
$547$	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
$552$	0.531213	+	0.702610i	0.0226099	+	0.0299051i
$553$	−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	$0.336530\pi$
$557$			41.1128i			1.74201i	−0.491278	+	0.871003i	$0.663470\pi$
$558$	2.57191	−	9.07852i	0.108878	−	0.384325i
$559$	−14.0214	−	3.62545i	−0.593043	−	0.153340i
$560$	−13.7041	−	18.8374i	−0.579103	−	0.796026i
$561$	−1.85230	−	14.8894i	−0.0782043	−	0.628633i
$562$	15.7000	−	27.1932i	0.662266	−	1.14708i
$563$	7.36906	+	12.7636i	0.310569	+	0.537921i	0.978486	−	0.206315i	$-0.0661471\pi$
$563$	7.36906	+	12.7636i	0.310569	+	0.537921i	−0.667917	+	0.744236i	$0.732814\pi$
$564$	−3.72803	−	4.93088i	−0.156978	−	0.207627i
$565$			4.11502i			0.173120i
$566$	−0.657780	+	1.13931i	−0.0276486	+	0.0478887i
$567$	−19.6471	+	13.4532i	−0.825102	+	0.564983i
$568$	−2.55784	+	4.43031i	−0.107325	+	0.185892i
$569$	20.8152	+	12.0176i	0.872617	+	0.503806i	0.868217	−	0.496185i	$-0.165266\pi$
$569$	20.8152	+	12.0176i	0.872617	+	0.503806i	0.00439981	+	0.999990i	$0.498599\pi$
$570$	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
$582$	−2.08120	+	0.258909i	−0.0862684	+	0.0107321i
$583$	−12.4590	+	21.5795i	−0.515997	+	0.893734i
$584$	−6.53543	+	11.3197i	−0.270438	+	0.468413i
$585$	−20.6849	−	0.113514i	−0.855216	−	0.00469323i
$586$	39.1598	−	22.6089i	1.61768	−	0.933966i
$587$	2.43294	+	4.21397i	0.100418	+	0.173929i	0.911857	−	0.410508i	$-0.134649\pi$
$587$	2.43294	+	4.21397i	0.100418	+	0.173929i	−0.811439	+	0.584437i	$0.801315\pi$
$588$	−0.845262	+	4.41535i	−0.0348580	+	0.182086i
$589$	−4.93820	+	8.55321i	−0.203475	+	0.352429i
$590$	9.94579	−	5.74220i	0.409462	−	0.236403i
$591$	−0.490560	−	3.94329i	−0.0201790	−	0.162205i
$592$	10.3902	+	17.9964i	0.427035	+	0.739646i
$593$	21.6766	+	37.5450i	0.890152	+	1.54179i	0.839692	+	0.543063i	$0.182736\pi$
$593$	21.6766	+	37.5450i	0.890152	+	1.54179i	0.0504606	+	0.998726i	$0.483931\pi$
$594$	−2.80094	+	18.2491i	−0.114924	+	0.748771i
$595$	18.8879	−	1.99707i	0.774330	−	0.0818719i
$596$	−3.32432	+	1.91930i	−0.136169	+	0.0786175i
$597$	4.14966	+	33.3563i	0.169834	+	1.36518i
$598$	0.788790	−	0.802757i	0.0322560	−	0.0328272i
$599$	−17.2985	−	9.98730i	−0.706798	−	0.408070i	0.103076	−	0.994673i	$-0.467131\pi$
$599$	−17.2985	−	9.98730i	−0.706798	−	0.408070i	−0.809874	+	0.586604i	$0.800465\pi$
$600$	−4.65436	+	3.51897i	−0.190014	+	0.143661i
$601$	−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
$606$	−29.7323	+	22.4793i	−1.20779	+	0.913160i
$607$		−	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
$609$	−0.881359	+	0.825540i	−0.0357145	+	0.0334526i
$610$	−31.9297			−1.29280
$611$	24.3236	−	24.7543i	0.984026	−	1.00145i
$612$	4.04839	−	1.02310i	0.163646	−	0.0413565i
$613$	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
$615$	−23.4595	−	31.0287i	−0.945977	−	1.25120i
$616$	−9.01019	−	12.3853i	−0.363031	−	0.499016i
$617$	37.9111	+	21.8880i	1.52625	+	0.881178i	0.999515	+	0.0311459i	$0.00991564\pi$
$617$	37.9111	+	21.8880i	1.52625	+	0.881178i	0.526731	+	0.850032i	$0.323418\pi$
$618$	−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
$621$	1.04119	+	0.159805i	0.0417814	+	0.00641276i
$622$	−17.1601	+	9.90738i	−0.688056	+	0.397250i
$623$	31.3010	−	3.30954i	1.25405	−	0.132594i
$624$	17.4659	−	22.8397i	0.699196	−	0.914318i
$625$	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
$630$	−23.0316	−	3.97064i	−0.917600	−	0.158194i
$631$	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
$633$	−28.4001	+	3.53307i	−1.12880	+	0.140427i
$634$	−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
$639$	1.49897	+	5.93140i	0.0592985	+	0.234642i
$640$			25.6444i			1.01369i
$641$	1.61326	−	0.931414i	0.0637198	−	0.0367886i	−0.467802	−	0.883833i	$-0.654954\pi$
$641$	1.61326	−	0.931414i	0.0637198	−	0.0367886i	0.531521	+	0.847045i	$0.321621\pi$
$642$	−34.4516	+	4.28591i	−1.35970	+	0.169151i
$643$	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	$-0.510827\pi$
$647$	−1.73007			−0.0680162			−0.0340081	+	0.999422i	$0.510827\pi$
$648$	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
$651$	8.95799	+	2.71704i	0.351091	+	0.106489i
$652$	4.08711	+	7.07909i	0.160064	+	0.277239i
$653$	20.3586	+	11.7540i	0.796693	+	0.459971i	0.842314	−	0.538988i	$-0.181193\pi$
$653$	20.3586	+	11.7540i	0.796693	+	0.459971i	−0.0456203	+	0.998959i	$0.514526\pi$
$654$	−6.25924	−	50.3139i	−0.244756	−	1.96743i
$655$	20.9541	−	36.2936i	0.818746	−	1.41811i
$656$	54.0696			2.11106
$657$	3.82997	+	15.1551i	0.149421	+	0.591255i
$658$	31.7082	−	23.0675i	1.23611	−	0.899264i
$659$	11.6929	+	6.75090i	0.455491	+	0.262978i	0.710146	−	0.704054i	$-0.248629\pi$
$659$	11.6929	+	6.75090i	0.455491	+	0.262978i	−0.254655	+	0.967032i	$0.581962\pi$
$660$	−2.26072	+	1.70923i	−0.0879984	+	0.0665318i
$661$		−	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
$663$	9.00687	+	21.6438i	0.349798	+	0.840575i
$664$		−	10.5243i		−	0.408423i
$665$	22.3539	+	9.93597i	0.866848	+	0.385300i
$666$	20.0592	+	5.68271i	0.777280	+	0.220201i
$667$	0.0534218			0.00206850
$668$	−3.56417	+	6.17332i	−0.137902	+	0.238853i
$669$	2.47266	+	19.8761i	0.0955986	+	0.768454i
$670$		−	17.0993i		−	0.660602i
$671$	−25.0237			−0.966030
$672$	6.92977	−	6.49089i	0.267322	−	0.250391i
$673$	−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
$675$	−1.05861	+	6.89724i	−0.0407460	+	0.265475i
$676$	−4.21608	−	2.33647i	−0.162157	−	0.0898642i
$677$	−12.3751	−	21.4343i	−0.475614	−	0.823788i	0.523995	−	0.851721i	$-0.324441\pi$
$677$	−12.3751	−	21.4343i	−0.475614	−	0.823788i	−0.999610	+	0.0279327i	$0.991108\pi$
$678$	−5.69477	+	0.708451i	−0.218706	+	0.0272079i
$679$	−0.218769	−	2.06907i	−0.00839557	−	0.0794038i
$680$	−15.5957	−	9.00418i	−0.598067	−	0.345294i
$681$	−1.90265	+	0.236697i	−0.0729097	+	0.00907025i
$682$	6.28577	−	3.62909i	0.240695	−	0.138965i
$683$	−10.8334	+	6.25466i	−0.414528	+	0.239328i	−0.692734	−	0.721194i	$-0.743594\pi$
$683$	−10.8334	+	6.25466i	−0.414528	+	0.239328i	0.278205	+	0.960522i	$0.410260\pi$
$684$	5.17449	+	1.46591i	0.197852	+	0.0560507i
$685$	−9.12672	−	5.26931i	−0.348714	−	0.201330i
$686$	−27.9042	−	5.87686i	−1.06539	−	0.224380i
$687$	−1.61371	−	12.9715i	−0.0615667	−	0.494894i
$688$	9.24671	+	16.0158i	0.352527	+	0.610595i
$689$	9.74608	−	37.6930i	0.371296	−	1.43599i
$690$	0.623531	+	0.824714i	0.0237374	+	0.0313963i
$691$	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
$693$	−18.0501	−	3.11184i	−0.685668	−	0.118209i
$694$	−36.8551			−1.39900
$695$			14.2357i			0.539993i
$696$	1.13623	−	0.141351i	0.0430686	−	0.00535790i
$697$	−22.0425	+	38.1788i	−0.834921	+	1.44612i
$698$	9.12464			0.345373
$699$	0.733120	+	5.89307i	0.0277291	+	0.222896i
$700$	0.775016	+	1.06533i	0.0292929	+	0.0402655i
$701$		−	36.4301i		−	1.37595i	−0.725736	−	0.687973i	$-0.758501\pi$
$701$		−	36.4301i		−	1.37595i	0.725736	−	0.687973i	$-0.241499\pi$
$702$	−3.40407	−	28.6454i	−0.128478	−	1.08115i
$703$	−18.8985	−	10.9111i	−0.712772	−	0.411519i
$704$			13.8872i			0.523395i
$705$	19.2275	+	25.4313i	0.724151	+	0.957799i
$706$	−12.6603	−	7.30941i	−0.476476	−	0.275093i
$707$	−21.7538	−	29.9024i	−0.818135	−	1.12460i
$708$	1.51063	+	1.99804i	0.0567731	+	0.0750909i
$709$	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
$711$	3.62933	−	12.8111i	0.136111	−	0.480452i
$712$	−25.8451	−	14.9217i	−0.968588	−	0.559214i
$713$	−0.207054	−	0.358629i	−0.00775425	−	0.0134308i
$714$	6.01553	+	25.7952i	0.225126	+	0.965360i
$715$	−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	$-0.487673\pi$
$719$	2.07634			0.0774345			0.0387172	+	0.999250i	$0.487673\pi$
$720$	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
$723$	1.87342	+	15.0592i	0.0696734	+	0.560058i
$724$	5.41331	−	3.12537i	0.201184	−	0.116154i
$725$			0.353887i			0.0131430i
$726$	12.0720	−	9.12711i	0.448033	−	0.338739i
$727$		−	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
$732$	−0.859733	−	6.91082i	−0.0317766	−	0.255431i
$733$	−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
$735$	4.35950	−	22.7725i	0.160802	−	0.839976i
$736$	−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
$741$	−3.89188	+	29.9420i	−0.142972	+	1.09995i
$742$	17.8666	−	40.1964i	0.655905	−	1.47565i
$743$	−1.45158	+	0.838068i	−0.0532531	+	0.0307457i	−0.526390	−	0.850243i	$-0.676455\pi$
$743$	−1.45158	+	0.838068i	−0.0532531	+	0.0307457i	0.473137	+	0.880989i	$0.343122\pi$
$744$	−5.35275	−	7.07982i	−0.196241	−	0.259559i
$745$	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
$750$	−25.8041	+	19.5094i	−0.942233	+	0.712382i
$751$	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
$753$	20.2805	+	26.8240i	0.739061	+	0.977520i
$754$	−0.391029	−	1.40974i	−0.0142404	−	0.0513396i
$755$	−6.08980			−0.221631
$756$	0.239257	−	5.09184i	0.00870171	−	0.185188i
$757$	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
$759$	0.488669	+	0.646339i	0.0177376	+	0.0234606i
$760$	−11.5971	−	20.0868i	−0.420671	−	0.728623i
$761$	−36.7323			−1.33155			−0.665773	−	0.746154i	$-0.731898\pi$
$761$	−36.7323			−1.33155			−0.665773	+	0.746154i	$0.731898\pi$
$762$	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
$765$	−20.8798	+	5.27673i	−0.754912	+	0.190780i
$766$	−41.0462	−	23.6981i	−1.48306	−	0.856246i
$767$	−9.85614	+	10.0307i	−0.355885	+	0.362186i
$768$	−14.8021	+	1.84144i	−0.534126	+	0.0664473i
$769$	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
$771$	15.8541	+	20.9695i	0.570972	+	0.755196i
$772$	−4.16457	−	7.21325i	−0.149886	−	0.259611i
$773$	−1.46891	−	2.54423i	−0.0528330	−	0.0915095i	0.838399	−	0.545056i	$-0.183492\pi$
$773$	−1.46891	−	2.54423i	−0.0528330	−	0.0915095i	−0.891232	+	0.453547i	$0.850158\pi$
$774$	17.8516	+	5.05730i	0.641663	+	0.181781i
$775$	2.37570	−	1.37161i	0.0853376	−	0.0492697i
$776$	−0.986360	+	1.70843i	−0.0354083	+	0.0613289i
$777$	−6.00336	+	19.7929i	−0.215370	+	0.710067i
$778$	6.15595	+	10.6624i	0.220702	+	0.382266i
$779$	−49.1731	+	28.3901i	−1.76181	+	1.01718i
$780$	2.68991	−	3.51751i	0.0963141	−	0.125947i
$781$	−2.35299	+	4.07549i	−0.0841965	+	0.145833i
$782$	0.585871	−	1.01476i	0.0209507	−	0.0362877i
$783$	0.856624	−	1.06825i	0.0306133	−	0.0381763i
$784$	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	−0.542095	−	0.840317i	$-0.682369\pi$
$797$	12.8929	−	22.3311i	0.456688	−	0.791007i	0.998784	+	0.0493097i	$0.0157021\pi$
$798$	−9.90188	+	32.6462i	−0.350523	+	1.15566i
$799$	18.0662	−	31.2916i	0.639137	−	1.10702i
$800$		−	2.78247i		−	0.0983752i
$801$	−34.6020	+	8.74458i	−1.22260	+	0.308975i
$802$	−14.4945	−	25.1052i	−0.511819	−	0.886497i
$803$	−6.01202	+	10.4131i	−0.212160	+	0.367471i
$804$	3.70094	−	0.460411i	0.130522	−	0.0162374i
$805$	−0.829433	+	0.603406i	−0.0292337	+	0.0212673i
$806$	−7.94821	+	8.08895i	−0.279964	+	0.284921i
$807$	−21.7436	+	2.70498i	−0.765410	+	0.0952199i
$808$			35.0607i			1.23343i
$809$			19.7954i			0.695968i	0.937500	+	0.347984i	$0.113134\pi$
$809$			19.7954i			0.695968i	−0.937500	+	0.347984i	$0.886866\pi$
$810$	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
$813$	14.8575	−	11.2331i	0.521076	−	0.393964i
$814$	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
$819$	28.4756	−	2.85288i	0.995019	−	0.0996876i
$820$	8.32720			0.290799
$821$	−31.5080	−	18.1912i	−1.09964	−	0.634877i	−0.163512	−	0.986541i	$-0.552282\pi$
$821$	−31.5080	−	18.1912i	−1.09964	−	0.634877i	−0.936126	+	0.351665i	$0.885616\pi$
$822$	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
$825$	−4.28160	+	3.23714i	−0.149066	+	0.112703i
$826$	−12.8485	+	9.34717i	−0.447056	+	0.325230i
$827$			10.4560i			0.363589i	0.983337	+	0.181795i	$0.0581906\pi$
$827$			10.4560i			0.363589i	−0.983337	+	0.181795i	$0.941809\pi$
$828$	−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
$831$	−9.05627	+	1.12663i	−0.314159	+	0.0390825i
$832$	−5.79953	−	20.9084i	−0.201063	−	0.724870i
$833$	−25.6962	+	5.49529i	−0.890322	+	0.190401i
$834$	−19.7008	+	2.45086i	−0.682184	+	0.0848663i
$835$	18.3824	−	31.8393i	0.636150	−	1.10184i
$836$	2.06847	+	3.58270i	0.0715397	+	0.123910i
$837$	−10.4915	−	1.61027i	−0.362639	−	0.0556591i
$838$		−	13.1235i		−	0.453342i
$839$	12.7055	−	22.0065i	0.438641	−	0.759749i	−0.558944	−	0.829206i	$-0.688793\pi$
$839$	12.7055	−	22.0065i	0.438641	−	0.759749i	0.997585	+	0.0694568i	$0.0221266\pi$
$840$	−16.0446	+	15.0285i	−0.553592	+	0.518531i
$841$	−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
$855$	−26.6878	−	7.56055i	−0.912703	−	0.258565i
$856$	−16.3280	+	28.2808i	−0.558078	+	0.966619i
$857$	18.2976	−	31.6923i	0.625033	−	1.08259i	−0.363502	−	0.931593i	$-0.618419\pi$
$857$	18.2976	−	31.6923i	0.625033	−	1.08259i	0.988535	−	0.150995i	$-0.0482477\pi$
$858$	13.4792	−	17.6263i	0.460172	−	0.601754i
$859$	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
$861$	36.7902	+	39.2778i	1.25381	+	1.33858i
$862$	14.4830	−	25.0852i	0.493292	−	0.854407i
$863$	10.5667	−	6.10069i	0.359695	−	0.207670i	−0.309252	−	0.950980i	$-0.600079\pi$
$863$	10.5667	−	6.10069i	0.359695	−	0.207670i	0.668947	+	0.743310i	$0.266745\pi$
$864$	−6.73529	+	8.39924i	−0.229139	+	0.285748i
$865$	3.63145	+	6.28986i	0.123473	+	0.213862i
$866$	8.50547	+	14.7319i	0.289028	+	0.500610i
$867$	−3.03791	−	4.01810i	−0.103173	−	0.136462i
$868$	−1.62048	+	1.17889i	−0.0550028	+	0.0400141i
$869$	8.87010	−	5.12115i	0.300898	−	0.173723i
$870$	1.33369	−	0.165916i	0.0452163	−	0.00562508i
$871$	5.59644	+	20.1762i	0.189628	+	0.683646i
$872$	−41.3020	−	23.8457i	−1.39866	−	0.807518i
$873$	0.578038	+	2.28728i	0.0195636	+	0.0774126i
$874$	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
$879$	−30.6764	−	40.5742i	−1.03469	−	1.36853i
$880$			20.3180i			0.684920i
$881$	−15.0907	−	26.1379i	−0.508420	−	0.880609i	−0.999952	−	0.00974960i	$-0.996897\pi$
$881$	−15.0907	−	26.1379i	−0.508420	−	0.880609i	0.491533	−	0.870859i	$-0.336437\pi$
$882$	32.2654	+	2.11254i	1.08643	+	0.0711329i
$883$	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
$885$	−7.79119	−	10.3050i	−0.261898	−	0.346400i
$886$	60.4431			2.03063
$887$	−1.60978	+	2.78822i	−0.0540511	+	0.0936192i	−0.891785	−	0.452459i	$-0.850547\pi$
$887$	−1.60978	+	2.78822i	−0.0540511	+	0.0936192i	0.837734	+	0.546079i	$0.183880\pi$
$888$	15.6430	−	11.8270i	0.524946	−	0.396890i
$889$	−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
$894$	16.6509	+	22.0233i	0.556889	+	0.736569i
$895$	−33.2995	+	19.2254i	−1.11308	+	0.642636i
$896$	−3.73052	−	35.2826i	−0.124628	−	1.17871i
$897$	−1.00566	−	0.769043i	−0.0335779	−	0.0256776i
$898$	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
$903$	−5.34266	+	17.6146i	−0.177793	+	0.586177i
$904$	−2.69898	+	4.67476i	−0.0897666	+	0.155480i
$905$	−27.9195	+	16.1193i	−0.928075	+	0.535824i
$906$	−1.04843	−	8.42768i	−0.0348319	−	0.279991i
$907$	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	$-0.650073\pi$
$911$		−	53.7798i		−	1.78180i	0.454196	−	0.890902i	$-0.349927\pi$
$912$	30.7551	−	23.2526i	1.01840	−	0.769972i
$913$		−	9.68144i		−	0.320409i
$914$	14.9056	−	8.60576i	0.493034	−	0.284653i
$915$	4.43413	+	35.6430i	0.146588	+	1.17832i
$916$	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
$924$	2.86174	−	2.68050i	0.0941444	−	0.0881820i
$925$	3.03061	+	5.24917i	0.0996458	+	0.172592i
$926$	53.5926	+	30.9417i	1.76116	+	1.01681i
$927$	13.1333	+	3.72063i	0.431355	+	0.122201i
$928$	−0.273003	+	0.472854i	−0.00896175	+	0.0155222i
$929$	−28.1976			−0.925133			−0.462567	−	0.886585i	$-0.653071\pi$
$929$	−28.1976			−0.925133			−0.462567	+	0.886585i	$0.653071\pi$
$930$	−6.28299	−	8.31020i	−0.206027	−	0.272502i
$931$	−32.2008	−	10.4184i	−1.05534	−	0.341451i
$932$	−1.10095	−	0.635635i	−0.0360629	−	0.0208209i
$933$	13.4426	+	17.7799i	0.440092	+	0.582087i
$934$		−	8.45124i		−	0.276533i
$935$	−14.3467	−	8.28304i	−0.469186	−	0.270884i
$936$	−23.4241	−	13.6959i	−0.765641	−	0.447663i
$937$			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
$939$	−5.53483	−	44.4909i	−0.180622	−	1.45190i
$940$	−6.82504			−0.222608
$941$	−11.6148	+	20.1174i	−0.378632	+	0.655810i	−0.990863	−	0.134869i	$-0.956939\pi$
$941$	−11.6148	+	20.1174i	−0.378632	+	0.655810i	0.612231	+	0.790679i	$0.290272\pi$
$942$	−50.5466	+	6.28819i	−1.64690	+	0.204880i
$943$		−	2.38074i		−	0.0775277i
$944$	17.9572			0.584457
$945$	−1.23399	+	26.2615i	−0.0401416	+	0.854286i
$946$	7.13608	+	12.3601i	0.232014	+	0.401860i
$947$	−1.36654	−	0.788973i	−0.0444066	−	0.0256382i	0.477632	−	0.878560i	$-0.341495\pi$
$947$	−1.36654	−	0.788973i	−0.0444066	−	0.0256382i	−0.522039	+	0.852922i	$0.674828\pi$
$948$	1.71906	+	2.27372i	0.0558325	+	0.0738469i
$949$	4.70293	−	18.1886i	0.152664	−	0.590426i
$950$	4.99865	+	8.65791i	0.162178	+	0.280900i
$951$	6.38245	+	51.3043i	0.206965	+	1.66366i
$952$	22.7670	+	10.1196i	0.737883	+	0.327977i
$953$	−32.1862	−	18.5827i	−1.04261	−	0.601954i	−0.122042	−	0.992525i	$-0.538944\pi$
$953$	−32.1862	−	18.5827i	−1.04261	−	0.601954i	−0.920573	+	0.390571i	$0.872278\pi$
$954$	−13.5952	+	47.9894i	−0.440162	+	1.55371i
$955$	15.9191	−	9.19090i	0.515130	−	0.297411i
$956$	−3.05647	+	1.76465i	−0.0988533	+	0.0570730i
$957$	1.04523	−	0.130030i	0.0337875	−	0.00420329i
$958$	22.7066	+	13.1097i	0.733617	+	0.423554i
$959$	13.3234	+	5.92205i	0.430236	+	0.191233i
$960$	19.7806	−	2.46078i	0.638415	−	0.0794212i
$961$	−13.4136	−	23.2331i	−0.432698	−	0.749454i
$962$	−17.8728	−	17.5618i	−0.576241	−	0.566214i
$963$	9.56869	+	37.8630i	0.308347	+	1.22012i
$964$	−2.81339	−	1.62431i	−0.0906131	−	0.0523155i
$965$	21.4791	+	37.2028i	0.691435	+	1.19760i
$966$	−0.977850	−	1.04397i	−0.0314618	−	0.0335891i
$967$	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
$969$	3.88087	+	31.1957i	0.124671	+	1.00215i
$970$	−1.15778	+	2.00533i	−0.0371740	+	0.0643872i
$971$	29.7526			0.954806			0.477403	−	0.878685i	$-0.341578\pi$
$971$	29.7526			0.954806			0.477403	+	0.878685i	$0.341578\pi$
$972$	0.549657	+	5.75378i	0.0176303	+	0.184552i
$973$	−2.07089	−	19.5861i	−0.0663896	−	0.627901i
$974$			16.3779i			0.524781i
$975$	5.09444	−	6.66186i	0.163153	−	0.213350i
$976$	−43.2370	−	24.9629i	−1.38398	−	0.799043i
$977$		−	30.2392i		−	0.967439i	−0.875223	−	0.483720i	$-0.839285\pi$
$977$		−	30.2392i		−	0.967439i	0.875223	−	0.483720i	$-0.160715\pi$
$978$	46.8983	−	35.4578i	1.49964	−	1.13382i
$979$	−23.7752	−	13.7266i	−0.759860	−	0.438705i
$980$	3.32581	+	3.68447i	0.106239	+	0.117696i
$981$	−55.2960	+	13.9743i	−1.76547	+	0.446166i
$982$	−8.73445			−0.278728
$983$	−1.67455	+	2.90041i	−0.0534099	+	0.0925086i	−0.891494	−	0.453032i	$-0.850342\pi$
$983$	−1.67455	+	2.90041i	−0.0534099	+	0.0925086i	0.838084	+	0.545541i	$0.183676\pi$
$984$	−6.29931	−	50.6360i	−0.200815	−	1.61422i
$985$	−3.79954	−	2.19367i	−0.121063	−	0.0698960i
$986$	−0.761577	−	1.31909i	−0.0242535	−	0.0420084i
$987$	−30.1535	−	32.1924i	−0.959797	−	1.02469i
$988$	−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
$996$	2.67373	−	0.332622i	0.0847204	−	0.0105395i
$997$	−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
$999$	3.55794	−	23.1812i	0.112568	−	0.733421i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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} +(2.12732 - 1.60838i) 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} +(0.637306 - 0.0792833i) q^{12} +(0.963713 + 3.47437i) q^{13} +(0.428341 + 4.05118i) q^{14} +(-3.28695 + 0.408909i) q^{15} +(2.30204 - 3.98726i) q^{16} +(1.87695 + 3.25097i) q^{17} +(-1.13178 - 4.47841i) q^{18} +4.83490i q^{19} +(0.354536 - 0.614074i) q^{20} +(4.46283 - 1.04075i) 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} +(0.303195 - 1.07024i) q^{36} +(-2.25673 + 3.90878i) q^{37} +(-3.72223 + 6.44709i) q^{38} +(6.19290 + 0.804955i) q^{39} +(-4.15454 + 2.39862i) q^{40} +(5.87191 + 10.1704i) q^{41} +(6.75220 + 2.04800i) q^{42} +(-2.00837 + 3.47860i) q^{43} +(0.741009 - 0.427822i) q^{44} +(-1.56375 + 5.51982i) q^{45} +(-0.156070 - 0.270321i) q^{46} +(-4.81266 - 8.33577i) q^{47} +(-4.80933 - 6.36107i) q^{48} +(-2.15484 + 6.66008i) q^{49} +(1.79071 - 1.03387i) q^{50} +(6.45220 - 0.802678i) q^{51} +(-0.936988 + 0.953580i) q^{52} +(-9.35130 - 5.39898i) q^{53} +(-7.90810 - 1.21376i) 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} +(-0.740681 - 0.979662i) q^{60} -10.8438i q^{61} +(1.57263 + 2.72388i) q^{62} +(1.34849 - 7.82187i) q^{63} -6.01791 q^{64} +(4.83258 - 4.91815i) q^{65} +(-3.71157 - 4.90911i) q^{66} +5.80716 q^{67} +(-0.695945 + 1.20541i) q^{68} +(-0.280085 + 0.211760i) 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} +(-1.40278 - 1.85539i) q^{75} +(-1.55253 + 0.896354i) q^{76} +(4.93720 - 3.59178i) q^{77} +(7.63822 + 5.84108i) 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} +(1.16157 + 1.24011i) q^{84} +(3.58938 - 6.21699i) q^{85} +(-5.35612 + 3.09236i) q^{86} +(0.0563475 + 0.452940i) 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} +(2.82226 - 2.13379i) q^{93} -14.8204i q^{94} +(8.00728 - 4.62301i) q^{95} +(-0.443038 - 3.56129i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more