LMFDB - Embedded newform 171.2.t.a.164.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(122,171)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("171.122"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			164.9
Character	$\chi$	$=$	171.164
Dual form			171.2.t.a.122.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.676405 q^{2} +(-1.39343 + 1.02876i) q^{3} -1.54248 q^{4} +(-0.120039 - 0.0693047i) q^{5} +(0.942525 - 0.695858i) q^{6} +(0.877021 - 1.51904i) q^{7} +2.39615 q^{8} +(0.883308 - 2.86701i) q^{9} +(0.0811952 + 0.0468781i) q^{10} +(-4.04328 - 2.33439i) q^{11} +(2.14934 - 1.58684i) q^{12} -6.55555i q^{13} +(-0.593221 + 1.02749i) q^{14} +(0.238565 - 0.0269201i) q^{15} +1.46419 q^{16} +(-4.06437 + 2.34656i) q^{17} +(-0.597474 + 1.93926i) q^{18} +(4.35516 + 0.180615i) q^{19} +(0.185158 + 0.106901i) q^{20} +(0.340662 + 3.01893i) q^{21} +(2.73489 + 1.57899i) q^{22} +1.08841i q^{23} +(-3.33887 + 2.46506i) q^{24} +(-2.49039 - 4.31349i) q^{25} +4.43421i q^{26} +(1.71864 + 4.90370i) q^{27} +(-1.35278 + 2.34309i) q^{28} +(-0.477136 - 0.826424i) q^{29} +(-0.161366 + 0.0182089i) q^{30} +(-5.38094 + 3.10669i) q^{31} -5.78268 q^{32} +(8.03556 - 0.906750i) q^{33} +(2.74916 - 1.58723i) q^{34} +(-0.210554 + 0.121563i) q^{35} +(-1.36248 + 4.42230i) q^{36} -4.68926i q^{37} +(-2.94585 - 0.122169i) q^{38} +(6.74408 + 9.13472i) q^{39} +(-0.287632 - 0.166064i) q^{40} +(3.88755 - 6.73343i) q^{41} +(-0.230426 - 2.04202i) q^{42} -1.08373 q^{43} +(6.23666 + 3.60074i) q^{44} +(-0.304729 + 0.282937i) q^{45} -0.736205i q^{46} +(-10.8483 + 6.26324i) q^{47} +(-2.04024 + 1.50629i) q^{48} +(1.96167 + 3.39771i) q^{49} +(1.68451 + 2.91767i) q^{50} +(3.24937 - 7.45103i) q^{51} +10.1118i q^{52} +(1.27386 - 2.20639i) q^{53} +(-1.16250 - 3.31689i) q^{54} +(0.323568 + 0.560437i) q^{55} +(2.10147 - 3.63986i) q^{56} +(-6.25442 + 4.22873i) q^{57} +(0.322737 + 0.558997i) q^{58} +(5.51548 - 9.55309i) q^{59} +(-0.367980 + 0.0415237i) q^{60} +(-0.556799 - 0.964404i) q^{61} +(3.63969 - 2.10138i) q^{62} +(-3.58044 - 3.85621i) q^{63} +0.983063 q^{64} +(-0.454331 + 0.786924i) q^{65} +(-5.43529 + 0.613330i) q^{66} -4.42825i q^{67} +(6.26919 - 3.61952i) q^{68} +(-1.11971 - 1.51662i) q^{69} +(0.142420 - 0.0822261i) q^{70} +(3.99931 + 6.92701i) q^{71} +(2.11654 - 6.86979i) q^{72} +(-0.561346 - 0.972280i) q^{73} +3.17184i q^{74} +(7.90774 + 3.44854i) q^{75} +(-6.71772 - 0.278594i) q^{76} +(-7.09208 + 4.09461i) q^{77} +(-4.56173 - 6.17877i) q^{78} +3.40591i q^{79} +(-0.175760 - 0.101475i) q^{80} +(-7.43954 - 5.06491i) q^{81} +(-2.62956 + 4.55452i) q^{82} +(3.07334 + 1.77440i) q^{83} +(-0.525464 - 4.65663i) q^{84} +0.650512 q^{85} +0.733037 q^{86} +(1.51505 + 0.660708i) q^{87} +(-9.68830 - 5.59354i) q^{88} +(7.79231 - 13.4967i) q^{89} +(0.206120 - 0.191380i) q^{90} +(-9.95817 - 5.74935i) q^{91} -1.67885i q^{92} +(4.30194 - 9.86465i) q^{93} +(7.33782 - 4.23649i) q^{94} +(-0.510272 - 0.323514i) q^{95} +(8.05777 - 5.94899i) q^{96} +14.5597i q^{97} +(-1.32688 - 2.29823i) q^{98} +(-10.2642 + 9.53015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} - 3 q^{3} + 30 q^{4} - 3 q^{5} - 11 q^{6} - q^{7} - 12 q^{8} + 5 q^{9} - 6 q^{10} - 9 q^{11} - 15 q^{12} - 3 q^{14} + 18 q^{15} + 18 q^{16} + 27 q^{17} - 6 q^{18} + q^{19} + 9 q^{20} + 6 q^{21}+ \cdots - 5 q^{99}+O(q^{100}) $ 36 * q - 6 * q^2 - 3 * q^3 + 30 * q^4 - 3 * q^5 - 11 * q^6 - q^7 - 12 * q^8 + 5 * q^9 - 6 * q^10 - 9 * q^11 - 15 * q^12 - 3 * q^14 + 18 * q^15 + 18 * q^16 + 27 * q^17 - 6 * q^18 + q^19 + 9 * q^20 + 6 * q^21 - 6 * q^22 - 5 * q^24 + 11 * q^25 - 9 * q^27 + 2 * q^28 - 12 * q^29 - 35 * q^30 - 12 * q^31 - 30 * q^32 - 21 * q^33 - 21 * q^34 - 15 * q^35 - 3 * q^36 - 36 * q^38 - 14 * q^39 - 30 * q^40 + 18 * q^41 - 26 * q^42 - 6 * q^43 - 66 * q^44 + 29 * q^45 + 45 * q^47 - 21 * q^48 - 9 * q^49 - 3 * q^50 - 36 * q^51 + 12 * q^53 + 38 * q^54 - 7 * q^55 - 6 * q^56 + 17 * q^57 - 6 * q^58 - 9 * q^59 + 75 * q^60 + 8 * q^61 + 12 * q^62 + 41 * q^63 + 12 * q^64 + 18 * q^65 + 11 * q^66 + 60 * q^68 + 51 * q^69 - 24 * q^70 - 9 * q^71 - 81 * q^72 - 18 * q^73 + 10 * q^76 - 6 * q^77 - 18 * q^78 + 12 * q^80 + 13 * q^81 - 9 * q^82 - 9 * q^83 + 96 * q^84 - 22 * q^85 + 102 * q^86 - 19 * q^87 - 3 * q^88 + 18 * q^89 + 15 * q^90 + 27 * q^91 + 17 * q^93 - 12 * q^94 - 21 * q^95 - 9 * q^96 + 84 * q^98 - 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.676405			−0.478291			−0.239145	−	0.970984i	$-0.576867\pi$
$2$	−0.676405			−0.478291			−0.239145	+	0.970984i	$0.576867\pi$
$3$	−1.39343	+	1.02876i	−0.804499	+	0.593955i
$3$	−1.39343	+	1.02876i	−0.804499	+	0.593955i
$4$	−1.54248			−0.771238
$5$	−0.120039	−	0.0693047i	−0.0536832	−	0.0309940i	0.472918	−	0.881106i	$-0.343201\pi$
$5$	−0.120039	−	0.0693047i	−0.0536832	−	0.0309940i	−0.526601	+	0.850112i	$0.676534\pi$
$6$	0.942525	−	0.695858i	0.384784	−	0.284083i
$7$	0.877021	−	1.51904i	0.331483	−	0.574145i	−0.651320	−	0.758803i	$-0.725784\pi$
$7$	0.877021	−	1.51904i	0.331483	−	0.574145i	0.982803	+	0.184658i	$0.0591178\pi$
$8$	2.39615			0.847167
$9$	0.883308	−	2.86701i	0.294436	−	0.955671i
$10$	0.0811952	+	0.0468781i	0.0256762	+	0.0148241i
$11$	−4.04328	−	2.33439i	−1.21909	−	0.703845i	−0.254370	−	0.967107i	$-0.581868\pi$
$11$	−4.04328	−	2.33439i	−1.21909	−	0.703845i	−0.964724	+	0.263262i	$0.915201\pi$
$12$	2.14934	−	1.58684i	0.620460	−	0.458080i
$13$		−	6.55555i		−	1.81818i	−0.416597	−	0.909091i	$-0.636777\pi$
$13$		−	6.55555i		−	1.81818i	0.416597	−	0.909091i	$-0.363223\pi$
$14$	−0.593221	+	1.02749i	−0.158545	+	0.274608i
$15$	0.238565	−	0.0269201i	0.0615971	−	0.00695075i
$16$	1.46419			0.366046
$17$	−4.06437	+	2.34656i	−0.985754	+	0.569125i	−0.904002	−	0.427528i	$-0.859385\pi$
$17$	−4.06437	+	2.34656i	−0.985754	+	0.569125i	−0.0817513	+	0.996653i	$0.526051\pi$
$18$	−0.597474	+	1.93926i	−0.140826	+	0.457089i
$19$	4.35516	+	0.180615i	0.999141	+	0.0414359i
$19$	4.35516	+	0.180615i	0.999141	+	0.0414359i
$20$	0.185158	+	0.106901i	0.0414025	+	0.0239038i
$21$	0.340662	+	3.01893i	0.0743386	+	0.658784i
$22$	2.73489	+	1.57899i	0.583081	+	0.336642i
$23$			1.08841i			0.226949i	0.993541	+	0.113474i	$0.0361980\pi$
$23$			1.08841i			0.226949i	−0.993541	+	0.113474i	$0.963802\pi$
$24$	−3.33887	+	2.46506i	−0.681544	+	0.503178i
$25$	−2.49039	−	4.31349i	−0.498079	−	0.862698i
$26$			4.43421i			0.869620i
$27$	1.71864	+	4.90370i	0.330752	+	0.943718i
$28$	−1.35278	+	2.34309i	−0.255652	+	0.442802i
$29$	−0.477136	−	0.826424i	−0.0886019	−	0.153463i	0.818318	−	0.574765i	$-0.194907\pi$
$29$	−0.477136	−	0.826424i	−0.0886019	−	0.153463i	−0.906920	+	0.421302i	$0.861573\pi$
$30$	−0.161366	+	0.0182089i	−0.0294613	+	0.00332448i
$31$	−5.38094	+	3.10669i	−0.966445	+	0.557977i	−0.898151	−	0.439688i	$-0.855089\pi$
$31$	−5.38094	+	3.10669i	−0.966445	+	0.557977i	−0.0682946	+	0.997665i	$0.521756\pi$
$32$	−5.78268			−1.02224
$33$	8.03556	−	0.906750i	1.39881	−	0.157845i
$34$	2.74916	−	1.58723i	0.471477	−	0.272207i
$35$	−0.210554	+	0.121563i	−0.0355901	+	0.0205480i
$36$	−1.36248	+	4.42230i	−0.227080	+	0.737050i
$37$		−	4.68926i		−	0.770909i	−0.922727	−	0.385455i	$-0.874045\pi$
$37$		−	4.68926i		−	0.770909i	0.922727	−	0.385455i	$-0.125955\pi$
$38$	−2.94585	−	0.122169i	−0.477880	−	0.0198184i
$39$	6.74408	+	9.13472i	1.07992	+	1.46273i
$40$	−0.287632	−	0.166064i	−0.0454786	−	0.0262571i
$41$	3.88755	−	6.73343i	0.607133	−	1.05158i	−0.384578	−	0.923092i	$-0.625653\pi$
$41$	3.88755	−	6.73343i	0.607133	−	1.05158i	0.991711	−	0.128492i	$-0.0410136\pi$
$42$	−0.230426	−	2.04202i	−0.0355555	−	0.315090i
$43$	−1.08373			−0.165267			−0.0826333	−	0.996580i	$-0.526333\pi$
$43$	−1.08373			−0.165267			−0.0826333	+	0.996580i	$0.526333\pi$
$44$	6.23666	+	3.60074i	0.940212	+	0.542832i
$45$	−0.304729	+	0.282937i	−0.0454264	+	0.0421778i
$46$		−	0.736205i		−	0.108548i
$47$	−10.8483	+	6.26324i	−1.58238	+	0.913588i	−0.587870	+	0.808955i	$0.700033\pi$
$47$	−10.8483	+	6.26324i	−1.58238	+	0.913588i	−0.994511	+	0.104633i	$0.966633\pi$
$48$	−2.04024	+	1.50629i	−0.294484	+	0.217415i
$49$	1.96167	+	3.39771i	0.280238	+	0.485387i
$50$	1.68451	+	2.91767i	0.238226	+	0.412620i
$51$	3.24937	−	7.45103i	0.455003	−	1.04335i
$52$			10.1118i			1.40225i
$53$	1.27386	−	2.20639i	0.174978	−	0.303071i	−0.765176	−	0.643822i	$-0.777348\pi$
$53$	1.27386	−	2.20639i	0.174978	−	0.303071i	0.940154	+	0.340751i	$0.110681\pi$
$54$	−1.16250	−	3.31689i	−0.158196	−	0.451371i
$55$	0.323568	+	0.560437i	0.0436299	+	0.0755693i
$56$	2.10147	−	3.63986i	0.280821	−	0.486396i
$57$	−6.25442	+	4.22873i	−0.828419	+	0.560109i
$58$	0.322737	+	0.558997i	0.0423775	+	0.0733999i
$59$	5.51548	−	9.55309i	0.718054	−	1.24371i	−0.243715	−	0.969847i	$-0.578366\pi$
$59$	5.51548	−	9.55309i	0.718054	−	1.24371i	0.961770	−	0.273860i	$-0.0883005\pi$
$60$	−0.367980	+	0.0415237i	−0.0475060	+	0.00536068i
$61$	−0.556799	−	0.964404i	−0.0712908	−	0.123479i	0.828176	−	0.560467i	$-0.189378\pi$
$61$	−0.556799	−	0.964404i	−0.0712908	−	0.123479i	−0.899467	+	0.436988i	$0.856045\pi$
$62$	3.63969	−	2.10138i	0.462242	−	0.266875i
$63$	−3.58044	−	3.85621i	−0.451093	−	0.485837i
$64$	0.983063			0.122883
$65$	−0.454331	+	0.786924i	−0.0563528	+	0.0976059i
$66$	−5.43529	+	0.613330i	−0.669038	+	0.0754957i
$67$		−	4.42825i		−	0.540996i	−0.962721	−	0.270498i	$-0.912812\pi$
$67$		−	4.42825i		−	0.540996i	0.962721	−	0.270498i	$-0.0871884\pi$
$68$	6.26919	−	3.61952i	0.760251	−	0.438931i
$69$	−1.11971	−	1.51662i	−0.134797	−	0.182580i
$70$	0.142420	−	0.0822261i	0.0170224	−	0.00982790i
$71$	3.99931	+	6.92701i	0.474631	+	0.822085i	0.999578	−	0.0290503i	$-0.00924829\pi$
$71$	3.99931	+	6.92701i	0.474631	+	0.822085i	−0.524947	+	0.851135i	$0.675915\pi$
$72$	2.11654	−	6.86979i	0.249436	−	0.809613i
$73$	−0.561346	−	0.972280i	−0.0657006	−	0.113797i	0.831304	−	0.555818i	$-0.187595\pi$
$73$	−0.561346	−	0.972280i	−0.0657006	−	0.113797i	−0.897005	+	0.442021i	$0.854262\pi$
$74$			3.17184i			0.368719i
$75$	7.90774	+	3.44854i	0.913107	+	0.398203i
$76$	−6.71772	−	0.278594i	−0.770576	−	0.0319569i
$77$	−7.09208	+	4.09461i	−0.808217	+	0.466625i
$78$	−4.56173	−	6.17877i	−0.516515	−	0.699608i
$79$			3.40591i			0.383195i	0.981474	+	0.191597i	$0.0613668\pi$
$79$			3.40591i			0.383195i	−0.981474	+	0.191597i	$0.938633\pi$
$80$	−0.175760	−	0.101475i	−0.0196505	−	0.0113452i
$81$	−7.43954	−	5.06491i	−0.826615	−	0.562768i
$82$	−2.62956	+	4.55452i	−0.290386	+	0.502963i
$83$	3.07334	+	1.77440i	0.337343	+	0.194765i	0.659097	−	0.752058i	$-0.270939\pi$
$83$	3.07334	+	1.77440i	0.337343	+	0.194765i	−0.321753	+	0.946824i	$0.604272\pi$
$84$	−0.525464	−	4.65663i	−0.0573328	−	0.508080i
$85$	0.650512			0.0705579
$86$	0.733037			0.0790454
$87$	1.51505	+	0.660708i	0.162430	+	0.0708353i
$88$	−9.68830	−	5.59354i	−1.03278	−	0.596273i
$89$	7.79231	−	13.4967i	0.825983	−	1.43065i	−0.0751819	−	0.997170i	$-0.523954\pi$
$89$	7.79231	−	13.4967i	0.825983	−	1.43065i	0.901165	−	0.433476i	$-0.142713\pi$
$90$	0.206120	−	0.191380i	0.0217270	−	0.0201732i
$91$	−9.95817	−	5.74935i	−1.04390	−	0.602696i
$92$		−	1.67885i		−	0.175032i
$93$	4.30194	−	9.86465i	0.446091	−	1.02292i
$94$	7.33782	−	4.23649i	0.756838	−	0.436961i
$95$	−0.510272	−	0.323514i	−0.0523528	−	0.0331918i
$96$	8.05777	−	5.94899i	0.822393	−	0.607166i
$97$			14.5597i			1.47832i	0.673532	+	0.739158i	$0.264776\pi$
$97$			14.5597i			1.47832i	−0.673532	+	0.739158i	$0.735224\pi$
$98$	−1.32688	−	2.29823i	−0.134035	−	0.232156i
$99$	−10.2642	+	9.53015i	−1.03159	+	0.957816i
$100$	3.84137	+	6.65345i	0.384137	+	0.665345i
$101$	6.51866	−	3.76355i	0.648631	−	0.374487i	−0.139300	−	0.990250i	$-0.544485\pi$
$101$	6.51866	−	3.76355i	0.648631	−	0.374487i	0.787932	+	0.615763i	$0.211152\pi$
$102$	−2.19789	+	5.03992i	−0.217624	+	0.499026i
$103$	−0.293683	+	0.169558i	−0.0289375	+	0.0167071i	−0.514399	−	0.857551i	$-0.671985\pi$
$103$	−0.293683	+	0.169558i	−0.0289375	+	0.0167071i	0.485461	+	0.874258i	$0.338652\pi$
$104$		−	15.7081i		−	1.54030i
$105$	0.168333	−	0.386000i	0.0164276	−	0.0376697i
$106$	−0.861646	+	1.49241i	−0.0836904	+	0.144956i
$107$	−11.8620			−1.14674			−0.573369	−	0.819297i	$-0.694364\pi$
$107$	−11.8620			−1.14674			−0.573369	+	0.819297i	$0.694364\pi$
$108$	−2.65096	−	7.56384i	−0.255089	−	0.727831i
$109$	8.94952	−	5.16701i	0.857209	−	0.494910i	−0.00586793	−	0.999983i	$-0.501868\pi$
$109$	8.94952	−	5.16701i	0.857209	−	0.494910i	0.863077	+	0.505073i	$0.168534\pi$
$110$	−0.218863	−	0.379082i	−0.0208678	−	0.0361441i
$111$	4.82412	+	6.53416i	0.457885	+	0.620195i
$112$	1.28412	−	2.22416i	0.121338	−	0.210164i
$113$	1.09234	+	1.89199i	0.102759	+	0.177983i	0.912820	−	0.408361i	$-0.133900\pi$
$113$	1.09234	+	1.89199i	0.102759	+	0.177983i	−0.810062	+	0.586345i	$0.800566\pi$
$114$	4.23052	−	2.86034i	0.396225	−	0.267895i
$115$	0.0754319	−	0.130652i	0.00703406	−	0.0121834i
$116$	0.735971	+	1.27474i	0.0683332	+	0.118357i
$117$	−18.7949	−	5.79057i	−1.73758	−	0.535338i
$118$	−3.73070	+	6.46176i	−0.343439	+	0.594853i
$119$			8.23194i			0.754621i
$120$	0.571636	−	0.0645046i	0.0521830	−	0.00588844i
$121$	5.39874	+	9.35088i	0.490794	+	0.850080i
$122$	0.376622	+	0.652328i	0.0340977	+	0.0590590i
$123$	1.51004	+	13.3819i	0.136156	+	1.20661i
$124$	8.29997	−	4.79199i	0.745360	−	0.430334i
$125$			1.38343i			0.123738i
$126$	2.42183	+	2.60836i	0.215754	+	0.232371i
$127$	−4.44199	−	2.56458i	−0.394163	−	0.227570i	0.289799	−	0.957087i	$-0.406411\pi$
$127$	−4.44199	−	2.56458i	−0.394163	−	0.227570i	−0.683962	+	0.729517i	$0.739745\pi$
$128$	10.9004			0.963469
$129$	1.51010	−	1.11489i	0.132957	−	0.0981608i
$130$	0.307312	−	0.532279i	0.0269530	−	0.0466840i
$131$	13.6250	+	7.86640i	1.19042	+	0.687290i	0.958402	−	0.285421i	$-0.0921334\pi$
$131$	13.6250	+	7.86640i	1.19042	+	0.687290i	0.232019	+	0.972711i	$0.425467\pi$
$132$	−12.3947	+	1.39864i	−1.07882	+	0.121736i
$133$	4.09392	−	6.45727i	0.354988	−	0.559917i
$134$			2.99529i			0.258753i
$135$	0.133545	−	0.707747i	0.0114938	−	0.0609131i
$136$	−9.73883	+	5.62271i	−0.835097	+	0.482144i
$137$	−2.84441	+	1.64222i	−0.243014	+	0.140304i	−0.616561	−	0.787307i	$-0.711475\pi$
$137$	−2.84441	+	1.64222i	−0.243014	+	0.140304i	0.373547	+	0.927611i	$0.378141\pi$
$138$	0.757378	+	1.02585i	0.0644723	+	0.0873264i
$139$	16.1681			1.37136			0.685681	−	0.727902i	$-0.259505\pi$
$139$	16.1681			1.37136			0.685681	+	0.727902i	$0.259505\pi$
$140$	0.324774	−	0.187509i	0.0274485	−	0.0158474i
$141$	8.67294	−	19.8877i	0.730393	−	1.67484i
$142$	−2.70515	−	4.68546i	−0.227011	−	0.393195i
$143$	−15.3032	+	26.5059i	−1.27972	+	2.21654i
$144$	1.29333	−	4.19784i	0.107777	−	0.349820i
$145$			0.132271i			0.0109845i
$146$	0.379698	+	0.657655i	0.0314240	+	0.0544279i
$147$	−6.22888	−	2.71639i	−0.513749	−	0.224044i
$148$			7.23307i			0.594555i
$149$	−5.19597	−	2.99989i	−0.425670	−	0.245761i	0.271830	−	0.962345i	$-0.412371\pi$
$149$	−5.19597	−	2.99989i	−0.425670	−	0.245761i	−0.697500	+	0.716584i	$0.745704\pi$
$150$	−5.34883	−	2.33261i	−0.436730	−	0.190457i
$151$	10.8923	+	6.28866i	0.886401	+	0.511764i	0.872764	−	0.488143i	$-0.162326\pi$
$151$	10.8923	+	6.28866i	0.886401	+	0.511764i	0.0136375	+	0.999907i	$0.495659\pi$
$152$	10.4356	+	0.432780i	0.846439	+	0.0351031i
$153$	3.13754	+	13.7253i	0.253655	+	1.10963i
$154$	4.79712	−	2.76962i	0.386563	−	0.223182i
$155$	0.861232			0.0691759
$156$	−10.4026	−	14.0901i	−0.832874	−	1.12811i
$157$	−7.88036	+	13.6492i	−0.628922	+	1.08932i	0.358847	+	0.933396i	$0.383170\pi$
$157$	−7.88036	+	13.6492i	−0.628922	+	1.08932i	−0.987768	+	0.155928i	$0.950163\pi$
$158$		−	2.30377i		−	0.183278i
$159$	0.494807	+	4.38495i	0.0392408	+	0.347749i
$160$	0.694149	+	0.400767i	0.0548773	+	0.0316834i
$161$	1.65334	+	0.954557i	0.130302	+	0.0752297i
$162$	5.03214	+	3.42593i	0.395362	+	0.269167i
$163$	−6.65366			−0.521155			−0.260578	−	0.965453i	$-0.583913\pi$
$163$	−6.65366			−0.521155			−0.260578	+	0.965453i	$0.583913\pi$
$164$	−5.99645	+	10.3861i	−0.468244	+	0.811022i
$165$	−1.02743	−	0.448057i	−0.0799849	−	0.0348812i
$166$	−2.07882	−	1.20021i	−0.161348	−	0.0931544i
$167$	4.21808			0.326404			0.163202	−	0.986593i	$-0.447818\pi$
$167$	4.21808			0.326404			0.163202	+	0.986593i	$0.447818\pi$
$168$	0.816278	+	7.23380i	0.0629772	+	0.558100i
$169$	−29.9752			−2.30579
$170$	−0.440009			−0.0337472
$171$	4.36477	−	12.3268i	0.333782	−	0.942650i
$172$	1.67162			0.127460
$173$	10.8955			0.828372			0.414186	−	0.910192i	$-0.364066\pi$
$173$	10.8955			0.828372			0.414186	+	0.910192i	$0.364066\pi$
$174$	−1.02479	−	0.446906i	−0.0776889	−	0.0338799i
$175$	−8.73651			−0.660418
$176$	−5.92011	−	3.41798i	−0.446245	−	0.257640i
$177$	2.14239	+	18.9857i	0.161032	+	1.42705i
$178$	−5.27076	+	9.12922i	−0.395060	+	0.684264i
$179$	−5.16954			−0.386390			−0.193195	−	0.981160i	$-0.561885\pi$
$179$	−5.16954			−0.386390			−0.193195	+	0.981160i	$0.561885\pi$
$180$	0.470038	−	0.436424i	0.0350345	−	0.0325291i
$181$	4.70681	+	2.71748i	0.349855	+	0.201989i	0.664621	−	0.747180i	$-0.268593\pi$
$181$	4.70681	+	2.71748i	0.349855	+	0.201989i	−0.314767	+	0.949169i	$0.601926\pi$
$182$	6.73576	+	3.88889i	0.499288	+	0.288264i
$183$	1.76800	+	0.771020i	0.130694	+	0.0569954i
$184$			2.60799i			0.192264i
$185$	−0.324988	+	0.562895i	−0.0238936	+	0.0413849i
$186$	−2.90986	+	6.67250i	−0.213361	+	0.489251i
$187$	21.9112			1.60230
$188$	16.7332	−	9.66091i	1.22039	−	0.704594i
$189$	8.95622	+	1.68996i	0.651469	+	0.122926i
$190$	0.345151	+	0.218826i	0.0250399	+	0.0158753i
$191$	−10.8662	−	6.27361i	−0.786251	−	0.453942i	0.0523898	−	0.998627i	$-0.483316\pi$
$191$	−10.8662	−	6.27361i	−0.786251	−	0.453942i	−0.838641	+	0.544684i	$0.816650\pi$
$192$	−1.36983	+	1.01134i	−0.0988591	+	0.0729868i
$193$	−0.103288	−	0.0596333i	−0.00743482	−	0.00429250i	0.496278	−	0.868164i	$-0.334700\pi$
$193$	−0.103288	−	0.0596333i	−0.00743482	−	0.00429250i	−0.503713	+	0.863871i	$0.668033\pi$
$194$		−	9.84827i		−	0.707065i
$195$	−0.176476	−	1.56392i	−0.0126377	−	0.111995i
$196$	−3.02583	−	5.24089i	−0.216131	−	0.374349i
$197$		−	14.8993i		−	1.06153i	−0.847519	−	0.530765i	$-0.821905\pi$
$197$		−	14.8993i		−	1.06153i	0.847519	−	0.530765i	$-0.178095\pi$
$198$	6.94274	−	6.44624i	0.493399	−	0.458115i
$199$	3.99752	−	6.92391i	0.283377	−	0.490823i	−0.688837	−	0.724916i	$-0.741879\pi$
$199$	3.99752	−	6.92391i	0.283377	−	0.490823i	0.972214	+	0.234093i	$0.0752120\pi$
$200$	−5.96735	−	10.3358i	−0.421956	−	0.730849i
$201$	4.55560	+	6.17046i	0.321327	+	0.435231i
$202$	−4.40926	+	2.54568i	−0.310234	+	0.179114i
$203$	−1.67383			−0.117480
$204$	−5.01208	+	11.4930i	−0.350916	+	0.804674i
$205$	−0.933316	+	0.538851i	−0.0651856	+	0.0376350i
$206$	0.198649	−	0.114690i	0.0138405	−	0.00799083i
$207$	3.12048	+	0.961400i	0.216889	+	0.0668219i
$208$		−	9.59854i		−	0.665539i
$209$	−17.1875	−	10.8969i	−1.18888	−	0.753754i
$210$	−0.113861	+	0.261092i	−0.00785718	+	0.0180171i
$211$	10.1008	+	5.83168i	0.695366	+	0.401470i	0.805619	−	0.592434i	$-0.201833\pi$
$211$	10.1008	+	5.83168i	0.695366	+	0.401470i	−0.110253	+	0.993904i	$0.535166\pi$
$212$	−1.96490	+	3.40331i	−0.134950	+	0.233740i
$213$	−12.6990	−	5.53799i	−0.870121	−	0.379457i
$214$	8.02348			0.548474
$215$	0.130090	+	0.0751073i	0.00887204	+	0.00512227i
$216$	4.11811	+	11.7500i	0.280202	+	0.799486i
$217$			10.8985i			0.739840i
$218$	−6.05350	+	3.49499i	−0.409995	+	0.236711i
$219$	1.78244	+	0.777317i	0.120446	+	0.0525262i
$220$	−0.499096	−	0.864460i	−0.0336491	−	0.0582819i
$221$	15.3830	+	26.6442i	1.03477	+	1.79228i
$222$	−3.26306	−	4.41974i	−0.219002	−	0.296634i
$223$		−	20.8438i		−	1.39581i	−0.716192	−	0.697903i	$-0.754116\pi$
$223$		−	20.8438i		−	1.39581i	0.716192	−	0.697903i	$-0.245884\pi$
$224$	−5.07153	+	8.78415i	−0.338856	+	0.586916i
$225$	−14.5666	+	3.32986i	−0.971108	+	0.221990i
$226$	−0.738865	−	1.27975i	−0.0491486	−	0.0851278i
$227$	11.9369	−	20.6753i	0.792279	−	1.37227i	−0.132274	−	0.991213i	$-0.542228\pi$
$227$	11.9369	−	20.6753i	0.792279	−	1.37227i	0.924553	−	0.381054i	$-0.124439\pi$
$228$	9.64730	−	6.52272i	0.638908	−	0.431978i
$229$	−8.94882	−	15.4998i	−0.591355	−	1.02426i	−0.994050	−	0.108923i	$-0.965260\pi$
$229$	−8.94882	−	15.4998i	−0.591355	−	1.02426i	0.402695	−	0.915334i	$-0.368073\pi$
$230$	−0.0510225	+	0.0883736i	−0.00336432	+	0.00582718i
$231$	5.66996	−	13.0016i	0.373056	−	0.855443i
$232$	−1.14329	−	1.98023i	−0.0750606	−	0.130009i
$233$	−1.17373	+	0.677654i	−0.0768936	+	0.0443946i	−0.537954	−	0.842974i	$-0.680803\pi$
$233$	−1.17373	+	0.677654i	−0.0768936	+	0.0443946i	0.461060	+	0.887369i	$0.347469\pi$
$234$	12.7129	+	3.91677i	0.831070	+	0.256047i
$235$	1.73629			0.113263
$236$	−8.50750	+	14.7354i	−0.553791	+	0.959194i
$237$	−3.50386	−	4.74590i	−0.227600	−	0.308280i
$238$		−	5.56812i		−	0.360928i
$239$	−6.15584	+	3.55408i	−0.398188	+	0.229894i	−0.685702	−	0.727882i	$-0.740505\pi$
$239$	−6.15584	+	3.55408i	−0.398188	+	0.229894i	0.287514	+	0.957777i	$0.407171\pi$
$240$	0.349303	−	0.0394161i	0.0225474	−	0.00254430i
$241$	14.3678	−	8.29527i	0.925513	−	0.534345i	0.0401234	−	0.999195i	$-0.487225\pi$
$241$	14.3678	−	8.29527i	0.925513	−	0.534345i	0.885390	+	0.464849i	$0.153892\pi$
$242$	−3.65173	−	6.32499i	−0.234742	−	0.406585i
$243$	15.5771	−	0.595883i	0.999269	−	0.0382259i
$244$	0.858849	+	1.48757i	0.0549822	+	0.0952319i
$245$		−	0.543812i		−	0.0347429i
$246$	−1.02140	−	9.05160i	−0.0651222	−	0.577109i
$247$	1.18403	−	28.5504i	0.0753380	−	1.81662i
$248$	−12.8935	+	7.44408i	−0.818740	+	0.472700i
$249$	−6.10792	+	0.689231i	−0.387074	+	0.0436782i
$250$		−	0.935760i		−	0.0591827i
$251$	−4.43373	−	2.55982i	−0.279855	−	0.161574i	0.353503	−	0.935433i	$-0.384990\pi$
$251$	−4.43373	−	2.55982i	−0.279855	−	0.161574i	−0.633358	+	0.773859i	$0.718324\pi$
$252$	5.52275	+	5.94812i	0.347900	+	0.374696i
$253$	2.54077	−	4.40074i	0.159737	−	0.276672i
$254$	3.00458	+	1.73470i	0.188524	+	0.108845i
$255$	−0.906444	+	0.669220i	−0.0567637	+	0.0419082i
$256$	−9.33922			−0.583701
$257$	−3.35771			−0.209448			−0.104724	−	0.994501i	$-0.533396\pi$
$257$	−3.35771			−0.209448			−0.104724	+	0.994501i	$0.533396\pi$
$258$	−1.02144	+	0.754119i	−0.0635919	+	0.0469494i
$259$	−7.12319	−	4.11258i	−0.442614	−	0.255543i
$260$	0.700794	−	1.21381i	0.0434614	−	0.0752774i
$261$	−2.79083	+	0.637969i	−0.172748	+	0.0394893i
$262$	−9.21602	−	5.32087i	−0.569367	−	0.328724i
$263$		−	28.1184i		−	1.73385i	−0.498437	−	0.866926i	$-0.666092\pi$
$263$		−	28.1184i		−	1.73385i	0.498437	−	0.866926i	$-0.333908\pi$
$264$	19.2544	−	2.17271i	1.18503	−	0.133721i
$265$	−0.305827	+	0.176569i	−0.0187868	+	0.0108466i
$266$	−2.76915	+	4.36773i	−0.169788	+	0.267803i
$267$	3.02678	+	26.8231i	0.185236	+	1.64155i
$268$			6.83046i			0.417237i
$269$	−4.97903	−	8.62394i	−0.303577	−	0.525811i	0.673366	−	0.739309i	$-0.264848\pi$
$269$	−4.97903	−	8.62394i	−0.303577	−	0.525811i	−0.976944	+	0.213498i	$0.931514\pi$
$270$	−0.0903308	+	0.478723i	−0.00549736	+	0.0291342i
$271$	2.04225	+	3.53729i	0.124058	+	0.214875i	0.921364	−	0.388700i	$-0.127076\pi$
$271$	2.04225	+	3.53729i	0.124058	+	0.214875i	−0.797306	+	0.603575i	$0.793742\pi$
$272$	−5.95099	+	3.43580i	−0.360832	+	0.208326i
$273$	19.7907	−	2.23323i	1.19779	−	0.135161i
$274$	1.92397	−	1.11081i	0.116232	−	0.0671063i
$275$			23.2542i			1.40228i
$276$	1.72713	+	2.33936i	0.103961	+	0.140813i
$277$	−7.84697	+	13.5914i	−0.471479	+	0.816626i	−0.999468	−	0.0326258i	$-0.989613\pi$
$277$	−7.84697	+	13.5914i	−0.471479	+	0.816626i	0.527989	+	0.849251i	$0.322946\pi$
$278$	−10.9362			−0.655909
$279$	4.15389	+	18.1714i	0.248687	+	1.08789i
$280$	−0.504519	+	0.291284i	−0.0301508	+	0.0174075i
$281$	3.42719	+	5.93607i	0.204449	+	0.354117i	0.949957	−	0.312380i	$-0.101126\pi$
$281$	3.42719	+	5.93607i	0.204449	+	0.354117i	−0.745508	+	0.666497i	$0.767793\pi$
$282$	−5.86642	+	13.4521i	−0.349340	+	0.801062i
$283$	−0.278438	+	0.482268i	−0.0165514	+	0.0286679i	−0.874182	−	0.485598i	$-0.838602\pi$
$283$	−0.278438	+	0.482268i	−0.0165514	+	0.0286679i	0.857631	+	0.514265i	$0.171935\pi$
$284$	−6.16884	−	10.6847i	−0.366053	−	0.634023i
$285$	1.04385	−	0.0741530i	0.0618322	−	0.00439245i
$286$	10.3512	−	17.9287i	0.612077	−	1.06015i
$287$	−6.81892	−	11.8107i	−0.402508	−	0.697164i
$288$	−5.10789	+	16.5790i	−0.300985	+	0.976928i
$289$	2.51272	−	4.35215i	0.147807	−	0.256009i
$290$		−	0.0894689i		−	0.00525379i
$291$	−14.9785	−	20.2880i	−0.878052	−	1.18930i
$292$	0.865863	+	1.49972i	0.0506708	+	0.0877644i
$293$	−2.27576	−	3.94172i	−0.132951	−	0.230278i	0.791862	−	0.610700i	$-0.209112\pi$
$293$	−2.27576	−	3.94172i	−0.132951	−	0.230278i	−0.924813	+	0.380422i	$0.875779\pi$
$294$	4.21325	+	1.83738i	0.245721	+	0.107158i
$295$	−1.32415	+	0.764498i	−0.0770949	+	0.0445108i
$296$		−	11.2362i		−	0.653088i
$297$	4.49821	−	23.8390i	0.261012	−	1.38328i
$298$	3.51458	+	2.02914i	0.203594	+	0.117545i
$299$	7.13512			0.412635
$300$	−12.1975	−	5.31929i	−0.704223	−	0.307109i
$301$	−0.950449	+	1.64623i	−0.0547830	+	0.0948869i
$302$	−7.36759	−	4.25368i	−0.423957	−	0.244772i
$303$	−5.21153	+	11.9504i	−0.299394	+	0.686532i
$304$	6.37676	+	0.264454i	0.365732	+	0.0151675i
$305$			0.154355i			0.00883835i
$306$	−2.12225	−	9.28388i	−0.121321	−	0.530724i
$307$	6.39989	−	3.69498i	0.365261	−	0.210883i	−0.306125	−	0.951991i	$-0.599033\pi$
$307$	6.39989	−	3.69498i	0.365261	−	0.210883i	0.671386	+	0.741108i	$0.265699\pi$
$308$	10.9394	−	6.31584i	0.623328	−	0.359879i
$309$	0.234793	−	0.538397i	0.0133569	−	0.0306284i
$310$	−0.582542			−0.0330862
$311$	−26.1635	+	15.1055i	−1.48360	+	0.856556i	−0.999826	−	0.0186380i	$-0.994067\pi$
$311$	−26.1635	+	15.1055i	−1.48360	+	0.856556i	−0.483772	+	0.875194i	$0.660734\pi$
$312$	16.1598	+	21.8881i	0.914870	+	1.23917i
$313$	−0.632333	−	1.09523i	−0.0357416	−	0.0619062i	0.847601	−	0.530634i	$-0.178046\pi$
$313$	−0.632333	−	1.09523i	−0.0357416	−	0.0619062i	−0.883343	+	0.468727i	$0.844713\pi$
$314$	5.33032	−	9.23238i	0.300807	−	0.521013i
$315$	0.162540	+	0.711039i	0.00915809	+	0.0400625i
$316$		−	5.25353i		−	0.295534i
$317$	7.05696	+	12.2230i	0.396358	+	0.686513i	0.993274	−	0.115792i	$-0.0369405\pi$
$317$	7.05696	+	12.2230i	0.396358	+	0.686513i	−0.596915	+	0.802304i	$0.703607\pi$
$318$	−0.334690	−	2.96600i	−0.0187685	−	0.166325i
$319$			4.45528i			0.249448i
$320$	−0.118006	−	0.0681309i	−0.00659675	−	0.00380863i
$321$	16.5288	−	12.2031i	0.922549	−	0.681110i
$322$	−1.11833	−	0.645667i	−0.0623220	−	0.0359816i
$323$	−18.1248	+	9.48556i	−1.00849	+	0.527791i
$324$	11.4753	+	7.81250i	0.637517	+	0.434028i
$325$	−28.2773	+	16.3259i	−1.56854	+	0.905598i
$326$	4.50057			0.249264
$327$	−7.15494	+	16.4068i	−0.395669	+	0.907297i
$328$	9.31514	−	16.1343i	0.514342	−	0.890867i
$329$			21.9720i			1.21135i
$330$	0.694955	+	0.303068i	0.0382560	+	0.0166833i
$331$	−15.7116	−	9.07108i	−0.863586	−	0.498592i	0.00162545	−	0.999999i	$-0.499483\pi$
$331$	−15.7116	−	9.07108i	−0.863586	−	0.498592i	−0.865212	+	0.501407i	$0.832816\pi$
$332$	−4.74056	−	2.73696i	−0.260172	−	0.150210i
$333$	−13.4442	−	4.14206i	−0.736736	−	0.226983i
$334$	−2.85313			−0.156116
$335$	−0.306898	+	0.531563i	−0.0167676	+	0.0290424i
$336$	0.498793	+	4.42027i	0.0272114	+	0.241146i
$337$	5.33828	+	3.08206i	0.290795	+	0.167890i	0.638300	−	0.769788i	$-0.279638\pi$
$337$	5.33828	+	3.08206i	0.290795	+	0.167890i	−0.347505	+	0.937678i	$0.612971\pi$
$338$	20.2754			1.10284
$339$	−3.46851	−	1.51260i	−0.188383	−	0.0821534i
$340$	−1.00340			−0.0544169
$341$	29.0089			1.57092
$342$	−2.95235	+	8.33788i	−0.159645	+	0.450861i
$343$	19.1600			1.03454
$344$	−2.59677			−0.140008
$345$	0.0293001	+	0.259656i	0.00157747	+	0.0139794i
$346$	−7.36979			−0.396202
$347$	−13.9949	−	8.07999i	−0.751288	−	0.433756i	0.0748709	−	0.997193i	$-0.476146\pi$
$347$	−13.9949	−	8.07999i	−0.751288	−	0.433756i	−0.826159	+	0.563437i	$0.809479\pi$
$348$	−2.33693	−	1.01913i	−0.125272	−	0.0546309i
$349$	11.5382	−	19.9847i	0.617624	−	1.06976i	−0.372294	−	0.928115i	$-0.621429\pi$
$349$	11.5382	−	19.9847i	0.617624	−	1.06976i	0.989918	−	0.141641i	$-0.0452379\pi$
$350$	5.90942			0.315872
$351$	32.1465	−	11.2666i	1.71585	−	0.601368i
$352$	23.3810	+	13.4990i	1.24621	+	0.719500i
$353$	26.3912	+	15.2370i	1.40466	+	0.810982i	0.994867	−	0.101196i	$-0.0322669\pi$
$353$	26.3912	+	15.2370i	1.40466	+	0.810982i	0.409795	+	0.912178i	$0.365600\pi$
$354$	−1.44912	−	12.8420i	−0.0770199	−	0.682546i
$355$		−	1.10868i		−	0.0588428i
$356$	−12.0195	+	20.8183i	−0.637030	+	1.10337i
$357$	−8.46868	−	11.4706i	−0.448210	−	0.607091i
$358$	3.49670			0.184806
$359$	−1.17054	+	0.675809i	−0.0617785	+	0.0356679i	−0.530571	−	0.847640i	$-0.678023\pi$
$359$	−1.17054	+	0.675809i	−0.0617785	+	0.0356679i	0.468793	+	0.883308i	$0.344689\pi$
$360$	−0.730177	+	0.677959i	−0.0384837	+	0.0357316i
$361$	18.9348	+	1.57321i	0.996566	+	0.0828006i
$362$	−3.18371	−	1.83812i	−0.167332	−	0.0966093i
$363$	−17.1426	−	7.47582i	−0.899752	−	0.392379i
$364$	15.3602	+	8.86824i	0.805096	+	0.464822i
$365$			0.155616i			0.00814530i
$366$	−1.19589	−	0.521521i	−0.0625099	−	0.0272604i
$367$	−0.793706	−	1.37474i	−0.0414311	−	0.0717608i	0.844566	−	0.535451i	$-0.179858\pi$
$367$	−0.793706	−	1.37474i	−0.0414311	−	0.0717608i	−0.885997	+	0.463690i	$0.846525\pi$
$368$			1.59363i			0.0830739i
$369$	−15.8709	−	17.0933i	−0.826207	−	0.889843i
$370$	0.219823	−	0.380745i	0.0114281	−	0.0197940i
$371$	−2.23440	−	3.87010i	−0.116004	−	0.200926i
$372$	−6.63564	+	15.2160i	−0.344042	+	0.788912i
$373$	−26.0140	+	15.0192i	−1.34695	+	0.777663i	−0.987817	−	0.155622i	$-0.950262\pi$
$373$	−26.0140	+	15.0192i	−1.34695	+	0.777663i	−0.359135	+	0.933285i	$0.616928\pi$
$374$	−14.8208			−0.766366
$375$	−1.42322	−	1.92772i	−0.0734947	−	0.0995469i
$376$	−25.9940	+	15.0077i	−1.34054	+	0.773961i
$377$	−5.41766	+	3.12789i	−0.279024	+	0.161095i
$378$	−6.05803	−	1.14310i	−0.311592	−	0.0587946i
$379$			20.4900i			1.05250i	0.850330	+	0.526250i	$0.176402\pi$
$379$			20.4900i			1.05250i	−0.850330	+	0.526250i	$0.823598\pi$
$380$	0.787083	+	0.499012i	0.0403765	+	0.0255988i
$381$	8.82795	−	0.996165i	0.452270	−	0.0510351i
$382$	7.34996	+	4.24350i	0.376057	+	0.217116i
$383$	14.8650	−	25.7469i	0.759565	−	1.31561i	−0.183507	−	0.983018i	$-0.558745\pi$
$383$	14.8650	−	25.7469i	0.759565	−	1.31561i	0.943073	−	0.332587i	$-0.107922\pi$
$384$	−15.1890	+	11.2139i	−0.775110	+	0.572257i
$385$	1.13510			0.0578503
$386$	0.0698644	+	0.0403362i	0.00355600	+	0.00205306i
$387$	−0.957263	+	3.10705i	−0.0486604	+	0.157940i
$388$		−	22.4580i		−	1.14013i
$389$	14.8922	−	8.59803i	0.755066	−	0.435938i	−0.0724554	−	0.997372i	$-0.523084\pi$
$389$	14.8922	−	8.59803i	0.755066	−	0.435938i	0.827521	+	0.561434i	$0.189750\pi$
$390$	0.119369	+	1.05784i	0.00604451	+	0.0535660i
$391$	−2.55402	−	4.42369i	−0.129162	−	0.223716i
$392$	4.70045	+	8.14142i	0.237409	+	0.411204i
$393$	−27.0781	+	3.05556i	−1.36591	+	0.154132i
$394$			10.0779i			0.507720i
$395$	0.236046	−	0.408843i	0.0118767	−	0.0205711i
$396$	15.8323	−	14.7000i	0.795601	−	0.738705i
$397$	−12.1112	−	20.9772i	−0.607844	−	1.05282i	−0.991595	−	0.129380i	$-0.958701\pi$
$397$	−12.1112	−	20.9772i	−0.607844	−	1.05282i	0.383751	−	0.923437i	$-0.374632\pi$
$398$	−2.70394	+	4.68337i	−0.135536	+	0.234756i
$399$	0.938374	+	13.2094i	0.0469775	+	0.661299i
$400$	−3.64640	−	6.31575i	−0.182320	−	0.315787i
$401$	8.70752	−	15.0819i	0.434833	−	0.753153i	−0.562449	−	0.826832i	$-0.690141\pi$
$401$	8.70752	−	15.0819i	0.434833	−	0.753153i	0.997282	+	0.0736792i	$0.0234741\pi$
$402$	−3.08143	−	4.17373i	−0.153688	−	0.208167i
$403$	20.3660	+	35.2750i	1.01450	+	1.75717i
$404$	−10.0549	+	5.80519i	−0.500249	+	0.288819i
$405$	0.542014	+	1.12358i	0.0269329	+	0.0558313i
$406$	1.13219			0.0561896
$407$	−10.9465	+	18.9600i	−0.542600	+	0.939811i
$408$	7.78597	−	17.8538i	0.385463	−	0.883894i
$409$			23.3316i			1.15367i	0.816859	+	0.576837i	$0.195713\pi$
$409$			23.3316i			1.15367i	−0.816859	+	0.576837i	$0.804287\pi$
$410$	0.631300	−	0.364481i	0.0311777	−	0.0180004i
$411$	2.27404	−	5.21454i	0.112170	−	0.257214i
$412$	0.453000	−	0.261539i	0.0223177	−	0.0128851i
$413$	−9.67438	−	16.7565i	−0.476045	−	0.824535i
$414$	−2.11071	−	0.650296i	−0.103736	−	0.0319603i
$415$	−0.245948	−	0.425994i	−0.0120731	−	0.0209112i
$416$			37.9086i			1.85862i
$417$	−22.5292	+	16.6331i	−1.10326	+	0.814527i
$418$	11.6257	+	7.37072i	0.568632	+	0.360514i
$419$	6.86848	−	3.96552i	0.335547	−	0.193728i	−0.322754	−	0.946483i	$-0.604609\pi$
$419$	6.86848	−	3.96552i	0.335547	−	0.193728i	0.658301	+	0.752755i	$0.271275\pi$
$420$	−0.259650	+	0.595395i	−0.0126696	+	0.0290523i
$421$			28.2153i			1.37513i	0.726123	+	0.687565i	$0.241320\pi$
$421$			28.2153i			1.37513i	−0.726123	+	0.687565i	$0.758680\pi$
$422$	−6.83221	−	3.94458i	−0.332587	−	0.192019i
$423$	8.37446	+	36.6345i	0.407180	+	1.78123i
$424$	3.05236	−	5.28684i	0.148236	−	0.256752i
$425$	20.2437	+	11.6877i	0.981966	+	0.566938i
$426$	8.58966	+	3.74592i	0.416170	+	0.181491i
$427$	−1.95330			−0.0945267
$428$	18.2968			0.884408
$429$	−5.94424	−	52.6775i	−0.286991	−	2.54329i
$430$	−0.0879933	−	0.0508029i	−0.00424341	−	0.00244994i
$431$	−3.39423	+	5.87899i	−0.163494	+	0.283181i	−0.936120	−	0.351682i	$-0.885610\pi$
$431$	−3.39423	+	5.87899i	−0.163494	+	0.283181i	0.772625	+	0.634863i	$0.218943\pi$
$432$	2.51641	+	7.17993i	0.121071	+	0.345444i
$433$	29.7286	+	17.1638i	1.42866	+	0.824839i	0.997015	−	0.0772030i	$-0.0245990\pi$
$433$	29.7286	+	17.1638i	1.42866	+	0.824839i	0.431648	+	0.902042i	$0.357932\pi$
$434$		−	7.37181i		−	0.353858i
$435$	−0.136075	−	0.184311i	−0.00652431	−	0.00883703i
$436$	−13.8044	+	7.96999i	−0.661112	+	0.381693i
$437$	−0.196583	+	4.74019i	−0.00940384	+	0.226754i
$438$	−1.20565	−	0.525781i	−0.0576083	−	0.0251228i
$439$			13.8023i			0.658747i	0.944200	+	0.329373i	$0.106837\pi$
$439$			13.8023i			0.658747i	−0.944200	+	0.329373i	$0.893163\pi$
$440$	0.775318	+	1.34289i	0.0369618	+	0.0640198i
$441$	11.4740	−	2.62291i	0.546383	−	0.124900i
$442$	−10.4051	−	18.0222i	−0.494922	−	0.857231i
$443$	23.3421	−	13.4766i	1.10902	−	0.640292i	0.170444	−	0.985367i	$-0.445480\pi$
$443$	23.3421	−	13.4766i	1.10902	−	0.640292i	0.938575	+	0.345075i	$0.112147\pi$
$444$	−7.44109	−	10.0788i	−0.353138	−	0.478318i
$445$	−1.87077	+	1.08009i	−0.0886829	+	0.0512011i
$446$			14.0989i			0.667601i
$447$	10.3264	−	1.16525i	0.488422	−	0.0551145i
$448$	0.862167	−	1.49332i	0.0407335	−	0.0705526i
$449$	−1.78199			−0.0840972			−0.0420486	−	0.999116i	$-0.513388\pi$
$449$	−1.78199			−0.0840972			−0.0420486	+	0.999116i	$0.513388\pi$
$450$	9.85293	−	2.25233i	0.464472	−	0.106176i
$451$	−31.4369	+	18.1501i	−1.48030	+	0.854654i
$452$	−1.68491	−	2.91835i	−0.0792515	−	0.137268i
$453$	−21.6472	+	2.44271i	−1.01707	+	0.114769i
$454$	−8.07417	+	13.9849i	−0.378940	+	0.656343i
$455$	0.796915	+	1.38030i	0.0373599	+	0.0647093i
$456$	−14.9865	+	10.1327i	−0.701809	+	0.474506i
$457$	−5.41688	+	9.38231i	−0.253391	+	0.438886i	−0.964457	−	0.264239i	$-0.914879\pi$
$457$	−5.41688	+	9.38231i	−0.253391	+	0.438886i	0.711066	+	0.703125i	$0.248213\pi$
$458$	6.05303	+	10.4842i	0.282839	+	0.489892i
$459$	−18.4920	−	15.8975i	−0.863133	−	0.742034i
$460$	−0.116352	+	0.201527i	−0.00542494	+	0.00939626i
$461$		−	20.7337i		−	0.965665i	−0.875713	−	0.482833i	$-0.839608\pi$
$461$		−	20.7337i		−	0.965665i	0.875713	−	0.482833i	$-0.160392\pi$
$462$	−3.83519	+	8.79436i	−0.178429	+	0.409150i
$463$	−13.1769	−	22.8231i	−0.612384	−	1.06068i	−0.990837	−	0.135060i	$-0.956877\pi$
$463$	−13.1769	−	22.8231i	−0.612384	−	1.06068i	0.378453	−	0.925620i	$-0.376456\pi$
$464$	−0.698616	−	1.21004i	−0.0324324	−	0.0561746i
$465$	−1.20007	+	0.886001i	−0.0556519	+	0.0410873i
$466$	0.793917	−	0.458368i	0.0367775	−	0.0212335i
$467$		−	12.0210i		−	0.556265i	−0.960543	−	0.278133i	$-0.910285\pi$
$467$		−	12.0210i		−	0.556265i	0.960543	−	0.278133i	$-0.0897155\pi$
$468$	28.9906	+	8.93181i	1.34009	+	0.412873i
$469$	−6.72670	−	3.88366i	−0.310610	−	0.179331i
$470$	−1.17444			−0.0541727
$471$	−3.06098	−	27.1262i	−0.141043	−	1.24991i
$472$	13.2159	−	22.8906i	0.608312	−	1.05363i
$473$	4.38180	+	2.52983i	0.201475	+	0.116322i
$474$	2.37003	+	3.21015i	0.108859	+	0.147447i
$475$	−10.0670	−	19.2357i	−0.461904	−	0.882595i
$476$		−	12.6976i		−	0.581992i
$477$	−5.20054	−	5.60110i	−0.238116	−	0.256457i
$478$	4.16384	−	2.40400i	0.190450	−	0.109956i
$479$	30.4077	−	17.5559i	1.38936	−	0.802149i	0.396119	−	0.918199i	$-0.370357\pi$
$479$	30.4077	−	17.5559i	1.38936	−	0.802149i	0.993243	+	0.116051i	$0.0370235\pi$
$480$	−1.37954	+	0.155671i	−0.0629672	+	0.00710535i
$481$	−30.7407			−1.40165
$482$	−9.71847	+	5.61096i	−0.442664	+	0.255572i
$483$	−3.28583	+	0.370780i	−0.149510	+	0.0168711i
$484$	−8.32742	−	14.4235i	−0.378519	−	0.655614i
$485$	1.00906	−	1.74774i	0.0458189	−	0.0793607i
$486$	−10.5364	+	0.403059i	−0.477941	+	0.0182831i
$487$		−	14.1105i		−	0.639409i	−0.947517	−	0.319705i	$-0.896416\pi$
$487$		−	14.1105i		−	0.639409i	0.947517	−	0.319705i	$-0.103584\pi$
$488$	−1.33417	−	2.31086i	−0.0603952	−	0.104608i
$489$	9.27143	−	6.84502i	0.419268	−	0.309542i
$490$			0.367837i			0.0166172i
$491$	−25.6095	−	14.7857i	−1.15574	−	0.667267i	−0.205461	−	0.978665i	$-0.565870\pi$
$491$	−25.6095	−	14.7857i	−1.15574	−	0.667267i	−0.950280	+	0.311398i	$0.899203\pi$
$492$	−2.32921	−	20.6413i	−0.105009	−	0.930582i
$493$	3.87851	+	2.23926i	0.174679	+	0.100851i
$494$	−0.800884	+	19.3117i	−0.0360335	+	0.868873i
$495$	1.89259	−	0.432637i	0.0850656	−	0.0194456i
$496$	−7.87869	+	4.54877i	−0.353764	+	0.204246i
$497$	14.0299			0.629327
$498$	4.13143	−	0.466199i	0.185134	−	0.0208909i
$499$	17.8745	−	30.9595i	0.800172	−	1.38594i	−0.119330	−	0.992855i	$-0.538075\pi$
$499$	17.8745	−	30.9595i	0.800172	−	1.38594i	0.919502	−	0.393084i	$-0.128592\pi$
$500$		−	2.13391i		−	0.0954314i
$501$	−5.87760	+	4.33939i	−0.262592	+	0.193869i
$502$	2.99900	+	1.73147i	0.133852	+	0.0772794i
$503$	−3.21576	−	1.85662i	−0.143384	−	0.0827826i	0.426592	−	0.904444i	$-0.359714\pi$
$503$	−3.21576	−	1.85662i	−0.143384	−	0.0827826i	−0.569976	+	0.821662i	$0.693047\pi$
$504$	−8.57927	−	9.24006i	−0.382151	−	0.411585i
$505$	−1.04333			−0.0464275
$506$	−1.71859	+	2.97668i	−0.0764006	+	0.132330i
$507$	41.7685	−	30.8373i	1.85500	−	1.36953i
$508$	6.85166	+	3.95581i	0.303993	+	0.175511i
$509$	34.9419			1.54877			0.774386	−	0.632714i	$-0.218059\pi$
$509$	34.9419			1.54877			0.774386	+	0.632714i	$0.218059\pi$
$510$	0.613123	−	0.452664i	0.0271496	−	0.0200443i
$511$	−1.96925			−0.0871145
$512$	−15.4837			−0.684291
$513$	6.59926	+	21.6668i	0.291364	+	0.956612i
$514$	2.27117			0.100177
$515$	0.0470047			0.00207128
$516$	−2.32929	+	1.71970i	−0.102541	+	0.0757054i
$517$	58.4834			2.57210
$518$	4.81816	+	2.78177i	0.211698	+	0.122224i
$519$	−15.1822	+	11.2089i	−0.666424	+	0.492015i
$520$	−1.08864	+	1.88559i	−0.0477402	+	0.0826884i
$521$	39.1773			1.71639			0.858195	−	0.513324i	$-0.171586\pi$
$521$	39.1773			1.71639			0.858195	+	0.513324i	$0.171586\pi$
$522$	1.88773	−	0.431526i	0.0826237	−	0.0188874i
$523$	−35.3599	−	20.4151i	−1.54618	−	0.892689i	−0.998428	−	0.0560491i	$-0.982150\pi$
$523$	−35.3599	−	20.4151i	−1.54618	−	0.892689i	−0.547754	−	0.836639i	$-0.684517\pi$
$524$	−21.0162	−	12.1337i	−0.918099	−	0.530064i
$525$	12.1737	−	8.98777i	0.531305	−	0.392258i
$526$			19.0194i			0.829285i
$527$	14.5801	−	25.2534i	0.635118	−	1.10006i
$528$	11.7655	−	1.32765i	0.512030	−	0.0577785i
$529$	21.8154			0.948494
$530$	0.206863	−	0.119432i	0.00898554	−	0.00518780i
$531$	−22.5170	−	24.2513i	−0.977154	−	1.05242i
$532$	−6.31478	+	9.96019i	−0.273780	+	0.431829i
$533$	−44.1413	−	25.4850i	−1.91197	−	1.10388i
$534$	−2.04733	−	18.1433i	−0.0885966	−	0.785137i
$535$	1.42390	+	0.822089i	0.0615606	+	0.0355420i
$536$		−	10.6107i		−	0.458314i
$537$	7.20340	−	5.31821i	0.310850	−	0.229498i
$538$	3.36784	+	5.83328i	0.145198	+	0.251490i
$539$		−	18.3172i		−	0.788977i
$540$	−0.205991	+	1.09168i	−0.00886443	+	0.0469785i
$541$	−14.5634	+	25.2245i	−0.626129	+	1.08449i	0.362192	+	0.932104i	$0.382028\pi$
$541$	−14.5634	+	25.2245i	−0.626129	+	1.08449i	−0.988321	+	0.152384i	$0.951305\pi$
$542$	−1.38139	−	2.39264i	−0.0593358	−	0.102773i
$543$	−9.35426	+	1.05555i	−0.401430	+	0.0452982i
$544$	23.5029	−	13.5694i	1.00768	−	0.581784i
$545$	−1.43239			−0.0613569
$546$	−13.3866	+	1.51057i	−0.572892	+	0.0646463i
$547$	−15.7898	+	9.11626i	−0.675124	+	0.389783i	−0.798015	−	0.602637i	$-0.794117\pi$
$547$	−15.7898	+	9.11626i	−0.675124	+	0.389783i	0.122891	+	0.992420i	$0.460783\pi$
$548$	4.38744	−	2.53309i	0.187422	−	0.108208i
$549$	−3.25678	+	0.744485i	−0.138996	+	0.0317738i
$550$		−	15.7292i		−	0.670697i
$551$	−1.92874	−	3.68538i	−0.0821670	−	0.157003i
$552$	−2.68299	−	3.63406i	−0.114196	−	0.154676i
$553$	5.17373	+	2.98705i	0.220009	+	0.127022i
$554$	5.30773	−	9.19326i	0.225504	−	0.390584i
$555$	−0.126235	−	1.11869i	−0.00535840	−	0.0474858i
$556$	−24.9389			−1.05765
$557$	−30.1772	−	17.4228i	−1.27865	−	0.738230i	−0.302051	−	0.953292i	$-0.597671\pi$
$557$	−30.1772	−	17.4228i	−1.27865	−	0.738230i	−0.976600	+	0.215062i	$0.931005\pi$
$558$	−2.80971	−	12.2912i	−0.118945	−	0.520329i
$559$			7.10441i			0.300485i
$560$	−0.308290	+	0.177991i	−0.0130276	+	0.00752151i
$561$	−30.5317	+	22.5413i	−1.28905	+	0.951695i
$562$	−2.31817	−	4.01519i	−0.0977862	−	0.169371i
$563$	13.2981	+	23.0329i	0.560446	+	0.970722i	0.997457	+	0.0712655i	$0.0227038\pi$
$563$	13.2981	+	23.0329i	0.560446	+	0.970722i	−0.437011	+	0.899456i	$0.643963\pi$
$564$	−13.3778	+	30.6762i	−0.563307	+	1.29170i
$565$		−	0.302818i		−	0.0127396i
$566$	0.188337	−	0.326209i	0.00791638	−	0.0137116i
$567$	−14.2185	+	6.85895i	−0.597119	+	0.288049i
$568$	9.58294	+	16.5981i	0.402091	+	0.696442i
$569$	−14.6846	+	25.4344i	−0.615610	+	1.06627i	0.374668	+	0.927159i	$0.377757\pi$
$569$	−14.6846	+	25.4344i	−0.615610	+	1.06627i	−0.990277	+	0.139108i	$0.955577\pi$
$570$	−0.706064	+	0.0501575i	−0.0295738	+	0.00210087i
$571$	0.947842	+	1.64171i	0.0396660	+	0.0687035i	0.885177	−	0.465255i	$-0.154037\pi$
$571$	0.947842	+	1.64171i	0.0396660	+	0.0687035i	−0.845511	+	0.533958i	$0.820704\pi$
$572$	23.6048	−	40.8847i	0.986967	−	1.70948i
$573$	21.5954	−	2.43687i	0.902159	−	0.101802i
$574$	4.61235	+	7.98882i	0.192516	+	0.333447i
$575$	4.69484	−	2.71057i	0.195788	−	0.113038i
$576$	0.868347	−	2.81845i	0.0361811	−	0.117436i
$577$	15.2421			0.634537			0.317268	−	0.948336i	$-0.397234\pi$
$577$	15.2421			0.634537			0.317268	+	0.948336i	$0.397234\pi$
$578$	−1.69961	+	2.94382i	−0.0706946	+	0.122447i
$579$	0.205273	−	0.0231634i	0.00853085	−	0.000962639i
$580$		−	0.204025i		−	0.00847168i
$581$	5.39077	−	3.11236i	0.223647	−	0.129123i
$582$	10.1315	+	13.7229i	0.419964	+	0.568832i
$583$	−10.3011	+	5.94737i	−0.426630	+	0.246315i
$584$	−1.34507	−	2.32973i	−0.0556594	−	0.0964049i
$585$	1.85481	+	1.99767i	0.0766868	+	0.0825934i
$586$	1.53933	+	2.66620i	0.0635892	+	0.110140i
$587$			41.8816i			1.72864i	0.502943	+	0.864319i	$0.332250\pi$
$587$			41.8816i			1.72864i	−0.502943	+	0.864319i	$0.667750\pi$
$588$	9.60790	+	4.18997i	0.396223	+	0.172792i
$589$	−23.9959	+	12.5582i	−0.988736	+	0.517453i
$590$	0.895661	−	0.517110i	0.0368738	−	0.0212891i
$591$	15.3278	+	20.7611i	0.630500	+	0.853999i
$592$		−	6.86594i		−	0.282189i
$593$	6.19893	+	3.57896i	0.254560	+	0.146970i	0.621850	−	0.783136i	$-0.286381\pi$
$593$	6.19893	+	3.57896i	0.254560	+	0.146970i	−0.367291	+	0.930106i	$0.619715\pi$
$594$	−3.04261	+	16.1248i	−0.124840	+	0.661609i
$595$	0.570512	−	0.988156i	0.0233887	−	0.0405105i
$596$	8.01465	+	4.62726i	0.328293	+	0.189540i
$597$	1.55276	+	13.7605i	0.0635504	+	0.563179i
$598$	−4.82623			−0.197359
$599$	−6.23274			−0.254663			−0.127331	−	0.991860i	$-0.540641\pi$
$599$	−6.23274			−0.254663			−0.127331	+	0.991860i	$0.540641\pi$
$600$	18.9481	+	8.26321i	0.773554	+	0.337344i
$601$	−19.8585	−	11.4653i	−0.810044	−	0.467679i	0.0369272	−	0.999318i	$-0.488243\pi$
$601$	−19.8585	−	11.4653i	−0.810044	−	0.467679i	−0.846971	+	0.531639i	$0.821576\pi$
$602$	0.642889	−	1.11352i	0.0262022	−	0.0453835i
$603$	−12.6958	−	3.91150i	−0.517015	−	0.159289i
$604$	−16.8011	−	9.70011i	−0.683626	−	0.394692i
$605$		−	1.49663i		−	0.0608467i
$606$	3.52510	−	8.08330i	0.143197	−	0.328362i
$607$	−1.44140	+	0.832190i	−0.0585044	+	0.0337775i	−0.528967	−	0.848642i	$-0.677420\pi$
$607$	−1.44140	+	0.832190i	−0.0585044	+	0.0337775i	0.470462	+	0.882420i	$0.344087\pi$
$608$	−25.1845	−	1.04444i	−1.02137	−	0.0423576i
$609$	2.33237	−	1.72197i	0.0945125	−	0.0697778i
$610$		−	0.104407i		−	0.00422730i
$611$	41.0590	+	71.1163i	1.66107	+	2.87706i
$612$	−4.83958	−	21.1710i	−0.195629	−	0.855787i
$613$	18.5832	+	32.1871i	0.750570	+	1.30003i	0.947547	+	0.319617i	$0.103554\pi$
$613$	18.5832	+	32.1871i	0.750570	+	1.30003i	−0.196977	+	0.980408i	$0.563112\pi$
$614$	−4.32891	+	2.49930i	−0.174701	+	0.100864i
$615$	0.746166	−	1.71101i	0.0300883	−	0.0689946i
$616$	−16.9937	+	9.81130i	−0.684695	+	0.395309i
$617$			15.6197i			0.628824i	0.949287	+	0.314412i	$0.101807\pi$
$617$			15.6197i			0.628824i	−0.949287	+	0.314412i	$0.898193\pi$
$618$	−0.158815	+	0.364175i	−0.00638849	+	0.0146493i
$619$	−17.0708	+	29.5674i	−0.686132	+	1.18842i	0.286948	+	0.957946i	$0.407359\pi$
$619$	−17.0708	+	29.5674i	−0.686132	+	1.18842i	−0.973080	+	0.230469i	$0.925974\pi$
$620$	−1.32843			−0.0533511
$621$	−5.33723	+	1.87058i	−0.214176	+	0.0750639i
$622$	17.6972	−	10.2175i	0.709591	−	0.409683i
$623$	−13.6680	−	23.6737i	−0.547598	−	0.948468i
$624$	9.87459	+	13.3749i	0.395300	+	0.535425i
$625$	−12.3561	+	21.4014i	−0.494244	+	0.856055i
$626$	0.427713	+	0.740821i	0.0170948	+	0.0296091i
$627$	35.1599	−	2.49769i	1.40415	−	0.0997483i
$628$	12.1553	−	21.0536i	0.485048	−	0.840128i
$629$	11.0036	+	19.0589i	0.438744	+	0.759927i
$630$	−0.109943	−	0.480950i	−0.00438023	−	0.0191615i
$631$	9.09528	−	15.7535i	0.362077	−	0.627136i	−0.626225	−	0.779642i	$-0.715401\pi$
$631$	9.09528	−	15.7535i	0.362077	−	0.627136i	0.988303	+	0.152506i	$0.0487343\pi$
$632$			8.16107i			0.324630i
$633$	−20.0741	+	2.26521i	−0.797875	+	0.0900340i
$634$	−4.77336	−	8.26771i	−0.189574	−	0.328353i
$635$	0.355476	+	0.615702i	0.0141066	+	0.0244334i
$636$	−0.763229	−	6.76369i	−0.0302640	−	0.268198i
$637$	22.2739	−	12.8598i	0.882522	−	0.509525i
$638$		−	3.01358i		−	0.119309i
$639$	23.3924	−	5.34740i	0.925391	−	0.211540i
$640$	−1.30848	−	0.755450i	−0.0517221	−	0.0298618i
$641$	−12.6220			−0.498539			−0.249269	−	0.968434i	$-0.580190\pi$
$641$	−12.6220			−0.498539			−0.249269	+	0.968434i	$0.580190\pi$
$642$	−11.1802	+	8.25424i	−0.441247	+	0.325769i
$643$	−13.2003	+	22.8636i	−0.520568	+	0.901651i	0.479146	+	0.877735i	$0.340947\pi$
$643$	−13.2003	+	22.8636i	−0.520568	+	0.901651i	−0.999714	+	0.0239155i	$0.992387\pi$
$644$	−2.55024	−	1.47238i	−0.100494	−	0.0580200i
$645$	−0.258538	+	0.0291740i	−0.0101799	+	0.00114873i
$646$	12.2597	−	6.41608i	0.482351	−	0.252437i
$647$			17.9111i			0.704159i	0.935970	+	0.352079i	$0.114525\pi$
$647$			17.9111i			0.704159i	−0.935970	+	0.352079i	$0.885475\pi$
$648$	−17.8262	−	12.1363i	−0.700281	−	0.476758i
$649$	−44.6013	+	25.7505i	−1.75075	+	1.01080i
$650$	19.1269	−	11.0429i	0.750219	−	0.433139i
$651$	−11.2120	−	15.1863i	−0.439431	−	0.595200i
$652$	10.2631			0.401935
$653$	3.92191	−	2.26431i	0.153476	−	0.0886094i	−0.421295	−	0.906924i	$-0.638424\pi$
$653$	3.92191	−	2.26431i	0.153476	−	0.0886094i	0.574771	+	0.818314i	$0.305091\pi$
$654$	4.83964	−	11.0976i	0.189245	−	0.433952i
$655$	−1.09036	−	1.88855i	−0.0426038	−	0.0737919i
$656$	5.69209	−	9.85898i	0.222239	−	0.384929i
$657$	−3.28338	+	0.750565i	−0.128097	+	0.0292823i
$658$		−	14.8620i		−	0.579380i
$659$	10.4986	+	18.1841i	0.408968	+	0.708353i	0.994774	−	0.102098i	$-0.0325554\pi$
$659$	10.4986	+	18.1841i	0.408968	+	0.708353i	−0.585806	+	0.810451i	$0.699222\pi$
$660$	1.58478	+	0.691117i	0.0616874	+	0.0269017i
$661$		−	19.1203i		−	0.743693i	−0.928294	−	0.371847i	$-0.878725\pi$
$661$		−	19.1203i		−	0.743693i	0.928294	−	0.371847i	$-0.121275\pi$
$662$	10.6274	+	6.13572i	0.413045	+	0.238472i
$663$	−48.8456	−	21.3014i	−1.89701	−	0.827278i
$664$	7.36419	+	4.25172i	0.285786	+	0.164999i
$665$	−0.938951	+	0.491398i	−0.0364110	+	0.0190556i
$666$	9.09370	+	2.80171i	0.352374	+	0.108564i
$667$	0.899487	−	0.519319i	0.0348283	−	0.0201081i
$668$	−6.50628			−0.251736
$669$	21.4433	+	29.0445i	0.829046	+	1.12292i
$670$	0.207588	−	0.359552i	0.00801981	−	0.0138907i
$671$			5.19914i			0.200711i
$672$	−1.96994	−	17.4575i	−0.0759922	−	0.673438i
$673$	−8.12324	−	4.68995i	−0.313128	−	0.180784i	0.335197	−	0.942148i	$-0.391197\pi$
$673$	−8.12324	−	4.68995i	−0.313128	−	0.180784i	−0.648325	+	0.761363i	$0.724530\pi$
$674$	−3.61084	−	2.08472i	−0.139084	−	0.0803004i
$675$	16.8720	−	19.6255i	0.649402	−	0.755385i
$676$	46.2361			1.77831
$677$	15.3198	−	26.5347i	0.588787	−	1.01981i	−0.405604	−	0.914049i	$-0.632939\pi$
$677$	15.3198	−	26.5347i	0.588787	−	1.01981i	0.994392	−	0.105761i	$-0.0337278\pi$
$678$	2.34611	+	1.02313i	0.0901020	+	0.0392932i
$679$	22.1169	+	12.7692i	0.848767	+	0.490036i
$680$	1.55872			0.0597743
$681$	4.63666	+	41.0898i	0.177677	+	1.57456i
$682$	−19.6217			−0.751355
$683$	−30.9867			−1.18567			−0.592837	−	0.805323i	$-0.701992\pi$
$683$	−30.9867			−1.18567			−0.592837	+	0.805323i	$0.701992\pi$
$684$	−6.73255	+	19.0137i	−0.257425	+	0.727008i
$685$	0.455255			0.0173944
$686$	−12.9599			−0.494812
$687$	28.4152	+	12.3918i	1.08411	+	0.472775i
$688$	−1.58677			−0.0604952
$689$	−14.4641	−	8.35086i	−0.551039	−	0.318142i
$690$	−0.0198187	−	0.175633i	−0.000754487	−	0.00668622i
$691$	8.00656	−	13.8678i	0.304584	−	0.527555i	−0.672585	−	0.740020i	$-0.734816\pi$
$691$	8.00656	−	13.8678i	0.304584	−	0.527555i	0.977169	+	0.212465i	$0.0681493\pi$
$692$	−16.8061			−0.638872
$693$	5.47483	+	23.9499i	0.207971	+	0.909781i
$694$	9.46625	+	5.46534i	0.359334	+	0.207462i
$695$	−1.94081	−	1.12053i	−0.0736191	−	0.0425040i
$696$	3.63028	+	1.58315i	0.137605	+	0.0600093i
$697$			36.4895i			1.38214i
$698$	−7.80447	+	13.5177i	−0.295404	+	0.511654i
$699$	0.938371	−	2.15175i	0.0354925	−	0.0813867i
$700$	13.4759			0.509340
$701$	29.7676	−	17.1863i	1.12431	−	0.649119i	0.181810	−	0.983334i	$-0.441804\pi$
$701$	29.7676	−	17.1863i	1.12431	−	0.649119i	0.942497	+	0.334215i	$0.108471\pi$
$702$	−21.7440	+	7.62080i	−0.820675	+	0.287628i
$703$	0.846950	−	20.4224i	0.0319433	−	0.770247i
$704$	−3.97480	−	2.29485i	−0.149806	−	0.0864904i
$705$	−2.41940	+	1.78622i	−0.0911200	+	0.0672731i
$706$	−17.8511	−	10.3064i	−0.671836	−	0.387885i
$707$		−	13.2029i		−	0.496544i
$708$	−3.30458	−	29.2850i	−0.124194	−	1.10060i
$709$	1.67597	+	2.90287i	0.0629425	+	0.109020i	0.895779	−	0.444499i	$-0.146618\pi$
$709$	1.67597	+	2.90287i	0.0629425	+	0.109020i	−0.832837	+	0.553518i	$0.813285\pi$
$710$			0.749920i			0.0281440i
$711$	9.76479	+	3.00847i	0.366208	+	0.112826i
$712$	18.6715	−	32.3401i	0.699746	−	1.21199i
$713$	−3.38135	−	5.85666i	−0.126632	−	0.219334i
$714$	5.72826	+	7.75880i	0.214375	+	0.290366i
$715$	3.67397	−	2.12117i	0.137399	−	0.0793272i
$716$	7.97389			0.297998
$717$	4.92146	−	11.2853i	0.183795	−	0.421455i
$718$	0.791756	−	0.457121i	0.0295481	−	0.0170596i
$719$	−21.7299	+	12.5458i	−0.810389	+	0.467878i	−0.847091	−	0.531448i	$-0.821648\pi$
$719$	−21.7299	+	12.5458i	−0.810389	+	0.467878i	0.0367021	+	0.999326i	$0.488315\pi$
$720$	−0.446180	+	0.414272i	−0.0166282	+	0.0154390i
$721$			0.594824i			0.0221524i
$722$	−12.8076	−	1.06413i	−0.476648	−	0.0396028i
$723$	−11.4868	+	26.3399i	−0.427197	+	0.979593i
$724$	−7.26015	−	4.19165i	−0.269821	−	0.155781i
$725$	−2.37651	+	4.11624i	−0.0882615	+	0.152873i
$726$	11.5953	+	5.05669i	0.430343	+	0.187671i
$727$	46.8522			1.73765			0.868825	−	0.495119i	$-0.164875\pi$
$727$	46.8522			1.73765			0.868825	+	0.495119i	$0.164875\pi$
$728$	−23.8613	−	13.7763i	−0.884357	−	0.510584i
$729$	−21.0926	+	16.8554i	−0.781206	+	0.624273i
$730$		−	0.105259i		−	0.00389582i
$731$	4.40466	−	2.54303i	0.162912	−	0.0940573i
$732$	−2.72710	−	1.18928i	−0.100797	−	0.0439570i
$733$	−11.0279	−	19.1009i	−0.407325	−	0.705508i	0.587264	−	0.809396i	$-0.300205\pi$
$733$	−11.0279	−	19.1009i	−0.407325	−	0.705508i	−0.994589	+	0.103888i	$0.966872\pi$
$734$	0.536867	+	0.929880i	0.0198161	+	0.0343225i
$735$	0.559452	+	0.757765i	0.0206357	+	0.0279506i
$736$		−	6.29392i		−	0.231997i
$737$	−10.3372	+	17.9046i	−0.380777	+	0.659526i
$738$	10.7352	+	11.5620i	0.395167	+	0.425604i
$739$	−6.35102	−	11.0003i	−0.233626	−	0.404652i	0.725247	−	0.688489i	$-0.241726\pi$
$739$	−6.35102	−	11.0003i	−0.233626	−	0.404652i	−0.958872	+	0.283837i	$0.908392\pi$
$740$	0.501286	−	0.868253i	0.0184276	−	0.0319176i
$741$	27.7217	+	41.0012i	1.01838	+	1.50622i
$742$	1.51136	+	2.61776i	0.0554839	+	0.0961009i
$743$	−13.6353	+	23.6170i	−0.500230	+	0.866423i	0.499770	+	0.866158i	$0.333418\pi$
$743$	−13.6353	+	23.6170i	−0.500230	+	0.866423i	−1.00000		0.000265368i	$0.999916\pi$
$744$	10.3081	−	23.6372i	0.377913	−	0.866581i
$745$	0.415813	+	0.720210i	0.0152342	+	0.0263865i
$746$	17.5960	−	10.1590i	0.644235	−	0.371949i
$747$	7.80192	−	7.24398i	0.285457	−	0.265043i
$748$	−33.7974			−1.23576
$749$	−10.4032	+	18.0188i	−0.380124	+	0.658394i
$750$	0.962672	+	1.30392i	0.0351518	+	0.0476124i
$751$		−	41.1874i		−	1.50295i	−0.659762	−	0.751475i	$-0.729343\pi$
$751$		−	41.1874i		−	1.50295i	0.659762	−	0.751475i	$-0.270657\pi$
$752$	−15.8839	+	9.17055i	−0.579225	+	0.334416i
$753$	8.81154	−	0.994313i	0.321111	−	0.0362348i
$754$	3.66453	−	2.11572i	0.133454	−	0.0770500i
$755$	−0.871668	−	1.50977i	−0.0317232	−	0.0549463i
$756$	−13.8148	−	2.60672i	−0.502438	−	0.0948056i
$757$	0.190902	+	0.330651i	0.00693844	+	0.0120177i	0.869474	−	0.493979i	$-0.164458\pi$
$757$	0.190902	+	0.330651i	0.00693844	+	0.0120177i	−0.862535	+	0.505997i	$0.831125\pi$
$758$		−	13.8595i		−	0.503401i
$759$	0.986915	+	8.74598i	0.0358227	+	0.317459i
$760$	−1.22269	−	0.775187i	−0.0443516	−	0.0281190i
$761$	−35.7329	+	20.6304i	−1.29532	+	0.747852i	−0.979592	−	0.200998i	$-0.935582\pi$
$761$	−35.7329	+	20.6304i	−1.29532	+	0.747852i	−0.315726	+	0.948850i	$0.602248\pi$
$762$	−5.97127	+	0.673811i	−0.216316	+	0.0244096i
$763$		−	18.1263i		−	0.656216i
$764$	16.7609	+	9.67689i	0.606387	+	0.350098i
$765$	0.574602	−	1.86503i	0.0207748	−	0.0674301i
$766$	−10.0547	+	17.4153i	−0.363293	+	0.629242i
$767$	−62.6258	−	36.1570i	−2.26129	−	1.30555i
$768$	13.0136	−	9.60781i	0.469587	−	0.346692i
$769$	17.0881			0.616214			0.308107	−	0.951352i	$-0.400305\pi$
$769$	17.0881			0.616214			0.308107	+	0.951352i	$0.400305\pi$
$770$	−0.767790			−0.0276692
$771$	4.67874	−	3.45428i	0.168501	−	0.124403i
$772$	0.159319	+	0.0919829i	0.00573402	+	0.00331054i
$773$	2.79674	−	4.84409i	0.100592	−	0.174230i	−0.811337	−	0.584579i	$-0.801260\pi$
$773$	2.79674	−	4.84409i	0.100592	−	0.174230i	0.911929	+	0.410349i	$0.134593\pi$
$774$	0.647497	−	2.10163i	0.0232738	−	0.0755414i
$775$	26.8013	+	15.4737i	0.962732	+	0.555833i
$776$			34.8873i			1.25238i
$777$	14.1565	−	1.59745i	0.507863	−	0.0573083i
$778$	−10.0732	+	5.81575i	−0.361141	+	0.208505i
$779$	18.1470	−	28.6230i	0.650184	−	1.02552i
$780$	0.272210	+	2.41231i	0.00974670	+	0.0863746i
$781$		−	37.3438i		−	1.33626i
$782$	1.72755	+	2.99221i	0.0617771	+	0.107001i
$783$	3.23251	−	3.76006i	0.115521	−	0.134373i
$784$	2.87225	+	4.97488i	0.102580	+	0.177674i
$785$	1.89191	−	1.09229i	0.0675251	−	0.0389856i
$786$	18.3158	−	2.06679i	0.653303	−	0.0737201i
$787$	5.68500	−	3.28224i	0.202648	−	0.116999i	−0.395242	−	0.918577i	$-0.629339\pi$
$787$	5.68500	−	3.28224i	0.202648	−	0.116999i	0.597890	+	0.801578i	$0.296006\pi$
$788$			22.9818i			0.818692i
$789$	28.9270	+	39.1810i	1.02983	+	1.39488i
$790$	−0.159662	+	0.276543i	−0.00568053	+	0.00983898i
$791$	3.83202			0.136251
$792$	−24.5945	+	22.8357i	−0.873928	+	0.811430i
$793$	−6.32220	+	3.65012i	−0.224508	+	0.129620i
$794$	8.19208	+	14.1891i	0.290726	+	0.503552i
$795$	0.244502	−	0.560659i	0.00867158	−	0.0198845i
$796$	−6.16608	+	10.6800i	−0.218551	+	0.378541i
$797$	−14.0122	−	24.2699i	−0.496339	−	0.859684i	0.503652	−	0.863906i	$-0.331989\pi$
$797$	−14.0122	−	24.2699i	−0.496339	−	0.859684i	−0.999991	+	0.00422263i	$0.998656\pi$
$798$	−0.634721	−	8.93493i	−0.0224689	−	0.316293i
$799$	29.3942	−	50.9122i	1.03989	−	1.80115i
$800$	14.4011	+	24.9435i	0.509158	+	0.881887i
$801$	−31.8122	−	34.2624i	−1.12403	−	1.21060i
$802$	−5.88981	+	10.2015i	−0.207976	+	0.360226i
$803$			5.24160i			0.184972i
$804$	−7.02690	−	9.51779i	−0.247820	−	0.335667i
$805$	−0.132311	−	0.229169i	−0.00466334	−	0.00807714i
$806$	−13.7757	−	23.8602i	−0.485228	−	0.840440i
$807$	15.8099	+	6.89465i	0.556535	+	0.242703i
$808$	15.6197	−	9.01803i	0.549499	−	0.317253i
$809$			32.3776i			1.13834i	0.822221	+	0.569168i	$0.192734\pi$
$809$			32.3776i			1.13834i	−0.822221	+	0.569168i	$0.807266\pi$
$810$	−0.366621	−	0.759997i	−0.0128818	−	0.0267036i
$811$	6.65521	+	3.84239i	0.233696	+	0.134924i	0.612276	−	0.790644i	$-0.290254\pi$
$811$	6.65521	+	3.84239i	0.233696	+	0.134924i	−0.378580	+	0.925569i	$0.623588\pi$
$812$	2.58185			0.0906051
$813$	−6.48476	−	2.82798i	−0.227431	−	0.0991817i
$814$	7.40430	−	12.8246i	0.259521	−	0.449503i
$815$	0.798701	+	0.461130i	0.0279773	+	0.0161527i
$816$	4.75768	−	10.9097i	0.166552	−	0.381916i
$817$	−4.71979	−	0.195737i	−0.165125	−	0.00684797i
$818$		−	15.7816i		−	0.551791i
$819$	−25.2796	+	23.4718i	−0.883341	+	0.820170i
$820$	1.43962	−	0.831164i	0.0502737	−	0.0290255i
$821$	−47.8717	+	27.6387i	−1.67073	+	0.964598i	−0.703505	+	0.710691i	$0.748383\pi$
$821$	−47.8717	+	27.6387i	−1.67073	+	0.964598i	−0.967228	+	0.253908i	$0.918284\pi$
$822$	−1.53817	+	3.52714i	−0.0536500	+	0.123023i
$823$	15.9381			0.555566			0.277783	−	0.960644i	$-0.410400\pi$
$823$	15.9381			0.555566			0.277783	+	0.960644i	$0.410400\pi$
$824$	−0.703709	+	0.406287i	−0.0245149	+	0.0141537i
$825$	−23.9230	−	32.4031i	−0.832891	−	1.12813i
$826$	6.54380	+	11.3342i	0.227688	+	0.394367i
$827$	−5.61139	+	9.71922i	−0.195127	+	0.337970i	−0.946942	−	0.321404i	$-0.895845\pi$
$827$	−5.61139	+	9.71922i	−0.195127	+	0.337970i	0.751815	+	0.659374i	$0.229179\pi$
$828$	−4.81327	−	1.48294i	−0.167273	−	0.0515356i
$829$		−	27.7051i		−	0.962238i	−0.876655	−	0.481119i	$-0.840231\pi$
$829$		−	27.7051i		−	0.962238i	0.876655	−	0.481119i	$-0.159769\pi$
$830$	0.166360	+	0.288145i	0.00577446	+	0.0100017i
$831$	−3.04801	−	27.0113i	−0.105734	−	0.937011i
$832$		−	6.44452i		−	0.223423i
$833$	−15.9459	−	9.20636i	−0.552492	−	0.318981i
$834$	15.2388	−	11.2507i	0.527678	−	0.389580i
$835$	−0.506335	−	0.292333i	−0.0175224	−	0.0101166i
$836$	26.5113	+	16.8082i	0.916912	+	0.581324i
$837$	−24.4822	−	21.0472i	−0.846227	−	0.727499i
$838$	−4.64587	+	2.68229i	−0.160489	+	0.0926583i
$839$	−39.0956			−1.34973			−0.674865	−	0.737941i	$-0.735798\pi$
$839$	−39.0956			−1.34973			−0.674865	+	0.737941i	$0.735798\pi$
$840$	0.403351	−	0.924913i	0.0139169	−	0.0319125i
$841$	14.0447	−	24.3261i	0.484299	−	0.838831i
$842$		−	19.0850i		−	0.657712i
$843$	−10.8824	−	4.74576i	−0.374808	−	0.163453i
$844$	−15.5802	−	8.99523i	−0.536293	−	0.309629i
$845$	3.59821	+	2.07743i	0.123782	+	0.0714656i
$846$	−5.66453	−	24.7797i	−0.194750	−	0.851945i
$847$	18.9392			0.650759
$848$	1.86517	−	3.23057i	0.0640501	−	0.110938i
$849$	−0.108154	−	0.958454i	−0.00371183	−	0.0328940i
$850$	−13.6930	−	7.90564i	−0.469665	−	0.271161i
$851$	5.10383			0.174957
$852$	19.5879	+	8.54222i	0.671070	+	0.292651i
$853$	5.97157			0.204463			0.102231	−	0.994761i	$-0.467402\pi$
$853$	5.97157			0.204463			0.102231	+	0.994761i	$0.467402\pi$
$854$	1.32122			0.0452112
$855$	−1.37825	+	1.17720i	−0.0471350	+	0.0402592i
$856$	−28.4230			−0.971478
$857$	50.4729			1.72412			0.862061	−	0.506804i	$-0.169173\pi$
$857$	50.4729			1.72412			0.862061	+	0.506804i	$0.169173\pi$
$858$	4.02072	+	35.6313i	0.137265	+	1.21643i
$859$	−12.8388			−0.438053			−0.219026	−	0.975719i	$-0.570288\pi$
$859$	−12.8388			−0.438053			−0.219026	+	0.975719i	$0.570288\pi$
$860$	−0.200660	−	0.115851i	−0.00684245	−	0.00395049i
$861$	21.6521	+	9.44240i	0.737901	+	0.321796i
$862$	2.29588	−	3.97658i	0.0781979	−	0.135443i
$863$	23.6047			0.803512			0.401756	−	0.915747i	$-0.368400\pi$
$863$	23.6047			0.803512			0.401756	+	0.915747i	$0.368400\pi$
$864$	−9.93834	−	28.3565i	−0.338109	−	0.964709i
$865$	−1.30789	−	0.755112i	−0.0444697	−	0.0256746i
$866$	−20.1085	−	11.6097i	−0.683316	−	0.394513i
$867$	0.976017	+	8.64941i	0.0331473	+	0.293749i
$868$		−	16.8107i		−	0.570592i
$869$	7.95071	−	13.7710i	0.269710	−	0.467151i
$870$	0.0920419	+	0.124669i	0.00312051	+	0.00422667i
$871$	−29.0296			−0.983630
$872$	21.4444	−	12.3809i	0.726198	−	0.419271i
$873$	41.7429	+	12.8607i	1.41278	+	0.435269i
$874$	0.132970	−	3.20629i	0.00449777	−	0.108454i
$875$	2.10149	+	1.21330i	0.0710435	+	0.0410170i
$876$	−2.74937	−	1.19899i	−0.0928927	−	0.0405102i
$877$	27.8434	+	16.0754i	0.940206	+	0.542828i	0.890025	−	0.455912i	$-0.150687\pi$
$877$	27.8434	+	16.0754i	0.940206	+	0.542828i	0.0501813	+	0.998740i	$0.484020\pi$
$878$		−	9.33593i		−	0.315072i
$879$	7.22620	+	3.15132i	0.243734	+	0.106291i
$880$	0.473764	+	0.820583i	0.0159706	+	0.0276619i
$881$		−	51.5651i		−	1.73727i	−0.495449	−	0.868637i	$-0.664997\pi$
$881$		−	51.5651i		−	1.73727i	0.495449	−	0.868637i	$-0.335003\pi$
$882$	−7.76110	+	1.77415i	−0.261330	+	0.0597387i
$883$	11.6957	−	20.2576i	0.393592	−	0.681722i	−0.599328	−	0.800504i	$-0.704565\pi$
$883$	11.6957	−	20.2576i	0.393592	−	0.681722i	0.992920	+	0.118781i	$0.0378988\pi$
$884$	−23.7279	−	41.0980i	−0.798057	−	1.38227i
$885$	1.05863	−	2.42751i	0.0355854	−	0.0815998i
$886$	−15.7887	+	9.11564i	−0.530433	+	0.306246i
$887$	−21.4014			−0.718587			−0.359294	−	0.933225i	$-0.616982\pi$
$887$	−21.4014			−0.718587			−0.359294	+	0.933225i	$0.616982\pi$
$888$	11.5593	+	15.6568i	0.387905	+	0.525409i
$889$	−7.79143	+	4.49839i	−0.261316	+	0.150871i
$890$	1.26540	−	0.730577i	0.0424162	−	0.0244890i
$891$	18.2567	+	37.8456i	0.611621	+	1.26788i
$892$			32.1511i			1.07650i
$893$	−48.3771	+	25.3180i	−1.61888	+	0.847236i
$894$	−6.98483	+	0.788183i	−0.233608	+	0.0263608i
$895$	0.620548	+	0.358274i	0.0207426	+	0.0119758i
$896$	9.55989	−	16.5582i	0.319373	−	0.553171i
$897$	−9.94231	+	7.34032i	−0.331964	+	0.245086i
$898$	1.20535			0.0402229
$899$	5.13488	+	2.96463i	0.171258	+	0.0988758i
$900$	22.4687	−	5.13622i	0.748955	−	0.171207i
$901$			11.9568i			0.398338i
$902$	21.2640	−	12.2768i	0.708015	−	0.408773i
$903$	−0.369184	−	3.27169i	−0.0122857	−	0.108875i
$904$	2.61741	+	4.53349i	0.0870538	+	0.150782i
$905$	−0.376668	−	0.652409i	−0.0125209	−	0.0216868i
$906$	14.6423	−	1.65226i	0.486456	−	0.0548928i
$907$		−	35.2140i		−	1.16926i	−0.811299	−	0.584631i	$-0.801239\pi$
$907$		−	35.2140i		−	1.16926i	0.811299	−	0.584631i	$-0.198761\pi$
$908$	−18.4124	+	31.8911i	−0.611036	+	1.05834i
$909$	−5.03217	−	22.0135i	−0.166907	−	0.730141i
$910$	−0.539037	−	0.933640i	−0.0178689	−	0.0309499i
$911$	5.48367	−	9.49800i	0.181682	−	0.314683i	−0.760771	−	0.649020i	$-0.775179\pi$
$911$	5.48367	−	9.49800i	0.181682	−	0.314683i	0.942454	+	0.334337i	$0.108512\pi$
$912$	−9.15764	+	6.19165i	−0.303240	+	0.205026i
$913$	−8.28426	−	14.3488i	−0.274169	−	0.474874i
$914$	3.66401	−	6.34624i	0.121195	−	0.209915i
$915$	−0.158794	−	0.215084i	−0.00524958	−	0.00711044i
$916$	13.8033	+	23.9081i	0.456075	+	0.789946i
$917$	23.8988	−	13.7980i	0.789208	−	0.455650i
$918$	12.5081	+	10.7532i	0.412829	+	0.354908i
$919$	−34.7810			−1.14732			−0.573659	−	0.819094i	$-0.694477\pi$
$919$	−34.7810			−1.14732			−0.573659	+	0.819094i	$0.694477\pi$
$920$	0.180746	−	0.313061i	0.00595902	−	0.0103213i
$921$	−5.11657	+	11.7326i	−0.168597	+	0.386604i
$922$			14.0244i			0.461869i
$923$	45.4103	−	26.2177i	1.49470	−	0.862965i
$924$	−8.74578	+	20.0547i	−0.287715	+	0.659750i
$925$	−20.2271	+	11.6781i	−0.665062	+	0.383973i
$926$	8.91295	+	15.4377i	0.292898	+	0.507314i
$927$	0.226713	+	0.991766i	0.00744623	+	0.0325739i
$928$	2.75913	+	4.77895i	0.0905727	+	0.156877i
$929$			36.6293i			1.20177i	0.799336	+	0.600885i	$0.205185\pi$
$929$			36.6293i			1.20177i	−0.799336	+	0.600885i	$0.794815\pi$
$930$	0.811733	−	0.599296i	0.0266178	−	0.0196517i
$931$	7.92970	+	15.1519i	0.259885	+	0.496582i
$932$	1.81045	−	1.04526i	0.0593033	−	0.0342388i
$933$	20.9172	−	47.9645i	0.684797	−	1.57029i
$934$			8.13106i			0.266056i
$935$	−2.63020	−	1.51855i	−0.0860167	−	0.0496618i
$936$	−45.0353	−	13.8751i	−1.47202	−	0.453521i
$937$	−7.00421	+	12.1317i	−0.228818	+	0.396324i	−0.957458	−	0.288573i	$-0.906819\pi$
$937$	−7.00421	+	12.1317i	−0.228818	+	0.396324i	0.728640	+	0.684897i	$0.240153\pi$
$938$	4.54998	+	2.62693i	0.148562	+	0.0857723i
$939$	2.00784	+	0.875614i	0.0655235	+	0.0285746i
$940$	−2.67819			−0.0873528
$941$	14.6106			0.476292			0.238146	−	0.971229i	$-0.423460\pi$
$941$	14.6106			0.476292			0.238146	+	0.971229i	$0.423460\pi$
$942$	2.07046	+	18.3483i	0.0674593	+	0.597820i
$943$	7.32872	+	4.23124i	0.238656	+	0.137788i
$944$	8.07569	−	13.9875i	0.262841	−	0.455254i
$945$	−0.957977	−	0.823570i	−0.0311630	−	0.0267907i
$946$	−2.96387	−	1.71119i	−0.0963638	−	0.0556357i
$947$		−	19.6671i		−	0.639094i	−0.947570	−	0.319547i	$-0.896469\pi$
$947$		−	19.6671i		−	0.639094i	0.947570	−	0.319547i	$-0.103531\pi$
$948$	5.40462	+	7.32045i	0.175534	+	0.237757i
$949$	−6.37383	+	3.67993i	−0.206903	+	0.119456i
$950$	6.80935	+	13.0111i	0.220924	+	0.422137i
$951$	−22.4079	−	9.77203i	−0.726627	−	0.316880i
$952$			19.7249i			0.639289i
$953$	−5.16671	−	8.94901i	−0.167366	−	0.289887i	0.770127	−	0.637891i	$-0.220193\pi$
$953$	−5.16671	−	8.94901i	−0.167366	−	0.289887i	−0.937493	+	0.348004i	$0.886860\pi$
$954$	3.51767	+	3.78861i	0.113889	+	0.122661i
$955$	0.869582	+	1.50616i	0.0281390	+	0.0487382i
$956$	9.49524	−	5.48208i	0.307098	−	0.177303i
$957$	−4.58342	−	6.20814i	−0.148161	−	0.200681i
$958$	−20.5679	+	11.8749i	−0.664519	+	0.383660i
$959$			5.76105i			0.186034i
$960$	0.234524	−	0.0264642i	0.00756923	−	0.000854128i
$961$	3.80301	−	6.58701i	0.122678	−	0.212484i
$962$	20.7931			0.670398
$963$	−10.4778	+	34.0084i	−0.337641	+	1.09590i
$964$	−22.1620	+	12.7953i	−0.713791	+	0.412107i
$965$	0.00826573	+	0.0143167i	0.000266083	+	0.000460870i
$966$	2.22255	−	0.250798i	0.0715094	−	0.00806928i
$967$	9.82237	−	17.0128i	0.315866	−	0.547096i	−0.663755	−	0.747950i	$-0.731038\pi$
$967$	9.82237	−	17.0128i	0.315866	−	0.547096i	0.979621	+	0.200854i	$0.0643716\pi$
$968$	12.9362	+	22.4061i	0.415784	+	0.720160i
$969$	15.4973	−	31.8635i	0.497844	−	1.02360i
$970$	−0.682532	+	1.18218i	−0.0219148	+	0.0379575i
$971$	−11.8669	−	20.5541i	−0.380828	−	0.659614i	0.610353	−	0.792130i	$-0.291028\pi$
$971$	−11.8669	−	20.5541i	−0.380828	−	0.659614i	−0.991181	+	0.132516i	$0.957694\pi$
$972$	−24.0273	+	0.919136i	−0.770674	+	0.0294813i
$973$	14.1798	−	24.5601i	0.454583	−	0.787360i
$974$			9.54444i			0.305823i
$975$	22.6071	−	51.8396i	0.724006	−	1.66019i
$976$	−0.815257	−	1.41207i	−0.0260957	−	0.0451991i
$977$	8.38318	+	14.5201i	0.268202	+	0.464539i	0.968397	−	0.249412i	$-0.0802373\pi$
$977$	8.38318	+	14.5201i	0.268202	+	0.464539i	−0.700196	+	0.713951i	$0.746904\pi$
$978$	−6.27124	+	4.63001i	−0.200532	+	0.148051i
$979$	−63.0130	+	36.3806i	−2.01390	+	1.16273i
$980$			0.838817i			0.0267950i
$981$	−6.90870	−	30.2225i	−0.220578	−	0.964929i
$982$	17.3224	+	10.0011i	0.552780	+	0.319148i
$983$	−8.58590			−0.273848			−0.136924	−	0.990582i	$-0.543722\pi$
$983$	−8.58590			−0.273848			−0.136924	+	0.990582i	$0.543722\pi$
$984$	3.61829	+	32.0651i	0.115347	+	1.02220i
$985$	−1.03259	+	1.78850i	−0.0329011	+	0.0569863i
$986$	−2.62344	−	1.51465i	−0.0835475	−	0.0482362i
$987$	−22.6039	−	30.6165i	−0.719490	−	0.974533i
$988$	−1.82634	+	44.0384i	−0.0581036	+	1.40105i
$989$		−	1.17954i		−	0.0375071i
$990$	−1.28016	+	0.292638i	−0.0406861	+	0.00930063i
$991$	10.7837	−	6.22600i	0.342557	−	0.197775i	−0.318845	−	0.947807i	$-0.603295\pi$
$991$	10.7837	−	6.22600i	0.342557	−	0.197775i	0.661402	+	0.750031i	$0.269962\pi$
$992$	31.1163	−	17.9650i	0.987942	−	0.570389i
$993$	31.2250	−	3.52349i	0.990895	−	0.111815i
$994$	−9.48990			−0.301001
$995$	−0.959719	+	0.554094i	−0.0304251	+	0.0175660i
$996$	9.42133	−	1.06312i	0.298526	−	0.0336863i
$997$	1.75449	+	3.03886i	0.0555652	+	0.0962417i	0.892470	−	0.451107i	$-0.148971\pi$
$997$	1.75449	+	3.03886i	0.0555652	+	0.0962417i	−0.836905	+	0.547348i	$0.815637\pi$
$998$	−12.0904	+	20.9412i	−0.382715	+	0.662881i
$999$	22.9947	−	8.05914i	0.727521	−	0.254980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.t.a.164.9	yes	36
3.2	odd	2		513.2.t.a.278.10		36
9.4	even	3		513.2.k.a.449.10		36
9.5	odd	6		171.2.k.a.50.9	✓	36
19.8	odd	6		171.2.k.a.65.9	yes	36
57.8	even	6		513.2.k.a.8.10		36
171.103	odd	6		513.2.t.a.179.10		36
171.122	even	6	inner	171.2.t.a.122.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.9	✓	36	9.5	odd	6
171.2.k.a.65.9	yes	36	19.8	odd	6
171.2.t.a.122.9	yes	36	171.122	even	6	inner
171.2.t.a.164.9	yes	36	1.1	even	1	trivial
513.2.k.a.8.10		36	57.8	even	6
513.2.k.a.449.10		36	9.4	even	3
513.2.t.a.179.10		36	171.103	odd	6
513.2.t.a.278.10		36	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.676405 q^{2} +(-1.39343 + 1.02876i) q^{3} -1.54248 q^{4} +(-0.120039 - 0.0693047i) q^{5} +(0.942525 - 0.695858i) q^{6} +(0.877021 - 1.51904i) q^{7} +2.39615 q^{8} +(0.883308 - 2.86701i) q^{9} +(0.0811952 + 0.0468781i) q^{10} +(-4.04328 - 2.33439i) q^{11} +(2.14934 - 1.58684i) q^{12} -6.55555i q^{13} +(-0.593221 + 1.02749i) q^{14} +(0.238565 - 0.0269201i) q^{15} +1.46419 q^{16} +(-4.06437 + 2.34656i) q^{17} +(-0.597474 + 1.93926i) q^{18} +(4.35516 + 0.180615i) q^{19} +(0.185158 + 0.106901i) q^{20} +(0.340662 + 3.01893i) q^{21} +(2.73489 + 1.57899i) q^{22} +1.08841i q^{23} +(-3.33887 + 2.46506i) q^{24} +(-2.49039 - 4.31349i) q^{25} +4.43421i q^{26} +(1.71864 + 4.90370i) q^{27} +(-1.35278 + 2.34309i) q^{28} +(-0.477136 - 0.826424i) q^{29} +(-0.161366 + 0.0182089i) q^{30} +(-5.38094 + 3.10669i) q^{31} -5.78268 q^{32} +(8.03556 - 0.906750i) q^{33} +(2.74916 - 1.58723i) q^{34} +(-0.210554 + 0.121563i) q^{35} +(-1.36248 + 4.42230i) q^{36} -4.68926i q^{37} +(-2.94585 - 0.122169i) q^{38} +(6.74408 + 9.13472i) q^{39} +(-0.287632 - 0.166064i) q^{40} +(3.88755 - 6.73343i) q^{41} +(-0.230426 - 2.04202i) q^{42} -1.08373 q^{43} +(6.23666 + 3.60074i) q^{44} +(-0.304729 + 0.282937i) q^{45} -0.736205i q^{46} +(-10.8483 + 6.26324i) q^{47} +(-2.04024 + 1.50629i) q^{48} +(1.96167 + 3.39771i) q^{49} +(1.68451 + 2.91767i) q^{50} +(3.24937 - 7.45103i) q^{51} +10.1118i q^{52} +(1.27386 - 2.20639i) q^{53} +(-1.16250 - 3.31689i) q^{54} +(0.323568 + 0.560437i) q^{55} +(2.10147 - 3.63986i) q^{56} +(-6.25442 + 4.22873i) q^{57} +(0.322737 + 0.558997i) q^{58} +(5.51548 - 9.55309i) q^{59} +(-0.367980 + 0.0415237i) q^{60} +(-0.556799 - 0.964404i) q^{61} +(3.63969 - 2.10138i) q^{62} +(-3.58044 - 3.85621i) q^{63} +0.983063 q^{64} +(-0.454331 + 0.786924i) q^{65} +(-5.43529 + 0.613330i) q^{66} -4.42825i q^{67} +(6.26919 - 3.61952i) q^{68} +(-1.11971 - 1.51662i) q^{69} +(0.142420 - 0.0822261i) q^{70} +(3.99931 + 6.92701i) q^{71} +(2.11654 - 6.86979i) q^{72} +(-0.561346 - 0.972280i) q^{73} +3.17184i q^{74} +(7.90774 + 3.44854i) q^{75} +(-6.71772 - 0.278594i) q^{76} +(-7.09208 + 4.09461i) q^{77} +(-4.56173 - 6.17877i) q^{78} +3.40591i q^{79} +(-0.175760 - 0.101475i) q^{80} +(-7.43954 - 5.06491i) q^{81} +(-2.62956 + 4.55452i) q^{82} +(3.07334 + 1.77440i) q^{83} +(-0.525464 - 4.65663i) q^{84} +0.650512 q^{85} +0.733037 q^{86} +(1.51505 + 0.660708i) q^{87} +(-9.68830 - 5.59354i) q^{88} +(7.79231 - 13.4967i) q^{89} +(0.206120 - 0.191380i) q^{90} +(-9.95817 - 5.74935i) q^{91} -1.67885i q^{92} +(4.30194 - 9.86465i) q^{93} +(7.33782 - 4.23649i) q^{94} +(-0.510272 - 0.323514i) q^{95} +(8.05777 - 5.94899i) q^{96} +14.5597i q^{97} +(-1.32688 - 2.29823i) q^{98} +(-10.2642 + 9.53015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} - 3 q^{3} + 30 q^{4} - 3 q^{5} - 11 q^{6} - q^{7} - 12 q^{8} + 5 q^{9} - 6 q^{10} - 9 q^{11} - 15 q^{12} - 3 q^{14} + 18 q^{15} + 18 q^{16} + 27 q^{17} - 6 q^{18} + q^{19} + 9 q^{20} + 6 q^{21}+ \cdots - 5 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 - 3 * q^3 + 30 * q^4 - 3 * q^5 - 11 * q^6 - q^7 - 12 * q^8 + 5 * q^9 - 6 * q^10 - 9 * q^11 - 15 * q^12 - 3 * q^14 + 18 * q^15 + 18 * q^16 + 27 * q^17 - 6 * q^18 + q^19 + 9 * q^20 + 6 * q^21 - 6 * q^22 - 5 * q^24 + 11 * q^25 - 9 * q^27 + 2 * q^28 - 12 * q^29 - 35 * q^30 - 12 * q^31 - 30 * q^32 - 21 * q^33 - 21 * q^34 - 15 * q^35 - 3 * q^36 - 36 * q^38 - 14 * q^39 - 30 * q^40 + 18 * q^41 - 26 * q^42 - 6 * q^43 - 66 * q^44 + 29 * q^45 + 45 * q^47 - 21 * q^48 - 9 * q^49 - 3 * q^50 - 36 * q^51 + 12 * q^53 + 38 * q^54 - 7 * q^55 - 6 * q^56 + 17 * q^57 - 6 * q^58 - 9 * q^59 + 75 * q^60 + 8 * q^61 + 12 * q^62 + 41 * q^63 + 12 * q^64 + 18 * q^65 + 11 * q^66 + 60 * q^68 + 51 * q^69 - 24 * q^70 - 9 * q^71 - 81 * q^72 - 18 * q^73 + 10 * q^76 - 6 * q^77 - 18 * q^78 + 12 * q^80 + 13 * q^81 - 9 * q^82 - 9 * q^83 + 96 * q^84 - 22 * q^85 + 102 * q^86 - 19 * q^87 - 3 * q^88 + 18 * q^89 + 15 * q^90 + 27 * q^91 + 17 * q^93 - 12 * q^94 - 21 * q^95 - 9 * q^96 + 84 * q^98 - 5 * q^99

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