LMFDB - Embedded newform 252.2.ba.a.155.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.21
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.246614 - 1.39255i) q^{2} +(0.483200 - 1.66329i) q^{3} +(-1.87836 - 0.686842i) q^{4} +(-3.28588 + 1.89710i) q^{5} +(-2.19704 - 1.08307i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.41969 + 2.44632i) q^{8} +(-2.53304 - 1.60740i) q^{9} +O(q^{10})$	\(q+(0.246614 - 1.39255i) q^{2} +(0.483200 - 1.66329i) q^{3} +(-1.87836 - 0.686842i) q^{4} +(-3.28588 + 1.89710i) q^{5} +(-2.19704 - 1.08307i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.41969 + 2.44632i) q^{8} +(-2.53304 - 1.60740i) q^{9} +(1.83146 + 5.04359i) q^{10} +(0.147235 - 0.255018i) q^{11} +(-2.05004 + 2.79237i) q^{12} +(-1.99299 - 3.45197i) q^{13} +(-0.909846 + 1.08267i) q^{14} +(1.56769 + 6.38203i) q^{15} +(3.05650 + 2.58028i) q^{16} -3.60857i q^{17} +(-2.86306 + 3.13096i) q^{18} -6.02570i q^{19} +(7.47508 - 1.30657i) q^{20} +(-1.25011 + 1.19885i) q^{21} +(-0.318814 - 0.267922i) q^{22} +(2.37532 + 4.11418i) q^{23} +(3.38294 + 3.54341i) q^{24} +(4.69800 - 8.13717i) q^{25} +(-5.29852 + 1.92403i) q^{26} +(-3.89752 + 3.43647i) q^{27} +(1.28329 + 1.53400i) q^{28} +(0.904457 + 0.522189i) q^{29} +(9.27388 - 0.609178i) q^{30} +(5.56802 - 3.21470i) q^{31} +(4.34693 - 3.61998i) q^{32} +(-0.353025 - 0.368119i) q^{33} +(-5.02510 - 0.889923i) q^{34} +3.79421 q^{35} +(3.65393 + 4.75907i) q^{36} -3.86636 q^{37} +(-8.39106 - 1.48602i) q^{38} +(-6.70462 + 1.64693i) q^{39} +(0.0240018 - 10.7316i) q^{40} +(-10.6945 + 6.17450i) q^{41} +(1.36116 + 2.03648i) q^{42} +(-0.852502 - 0.492192i) q^{43} +(-0.451718 + 0.377890i) q^{44} +(11.3726 + 0.476285i) q^{45} +(6.31496 - 2.29313i) q^{46} +(1.68371 - 2.91626i) q^{47} +(5.76863 - 3.83704i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-10.1728 - 8.54892i) q^{50} +(-6.00208 - 1.74366i) q^{51} +(1.37261 + 7.85292i) q^{52} -2.03029i q^{53} +(3.82425 + 6.27496i) q^{54} +1.11728i q^{55} +(2.45265 - 1.40873i) q^{56} +(-10.0225 - 2.91162i) q^{57} +(0.950223 - 1.13072i) q^{58} +(-4.15275 - 7.19278i) q^{59} +(1.43876 - 13.0645i) q^{60} +(-5.48589 + 9.50184i) q^{61} +(-3.10346 - 8.54650i) q^{62} +(1.38997 + 2.65857i) q^{63} +(-3.96897 - 6.94603i) q^{64} +(13.0975 + 7.56183i) q^{65} +(-0.599682 + 0.400819i) q^{66} +(9.26153 - 5.34715i) q^{67} +(-2.47852 + 6.77821i) q^{68} +(7.99081 - 1.96287i) q^{69} +(0.935704 - 5.28360i) q^{70} +2.73284 q^{71} +(7.52833 - 3.91461i) q^{72} +8.63292 q^{73} +(-0.953498 + 5.38408i) q^{74} +(-11.2644 - 11.7460i) q^{75} +(-4.13870 + 11.3185i) q^{76} +(-0.255018 + 0.147235i) q^{77} +(0.639970 + 9.74264i) q^{78} +(4.74756 + 2.74100i) q^{79} +(-14.9383 - 2.67999i) q^{80} +(3.83254 + 8.14319i) q^{81} +(5.96084 + 16.4153i) q^{82} +(4.07096 - 7.05111i) q^{83} +(3.17157 - 1.39325i) q^{84} +(6.84583 + 11.8573i) q^{85} +(-0.895639 + 1.06577i) q^{86} +(1.30558 - 1.25205i) q^{87} +(0.414829 + 0.722231i) q^{88} -3.35572i q^{89} +(3.46790 - 15.7195i) q^{90} +3.98599i q^{91} +(-1.63593 - 9.35939i) q^{92} +(-2.65649 - 10.8145i) q^{93} +(-3.64580 - 3.06383i) q^{94} +(11.4314 + 19.7997i) q^{95} +(-3.92062 - 8.97935i) q^{96} +(6.74076 - 11.6753i) q^{97} +(1.32929 - 0.482699i) q^{98} +(-0.782868 + 0.409306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.246614	−	1.39255i	0.174382	−	0.984678i
$2$	0.246614	−	1.39255i	0.174382	−	0.984678i
$3$	0.483200	−	1.66329i	0.278975	−	0.960298i
$3$	0.483200	−	1.66329i	0.278975	−	0.960298i
$4$	−1.87836	−	0.686842i	−0.939182	−	0.343421i
$5$	−3.28588	+	1.89710i	−1.46949	+	0.848410i	−0.999414	−	0.0342161i	$-0.989107\pi$
$5$	−3.28588	+	1.89710i	−1.46949	+	0.848410i	−0.470075	+	0.882626i	$0.655773\pi$
$6$	−2.19704	−	1.08307i	−0.896936	−	0.442160i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	−1.41969	+	2.44632i	−0.501936	+	0.864905i
$9$	−2.53304	−	1.60740i	−0.844345	−	0.535799i
$10$	1.83146	+	5.04359i	0.579158	+	1.59492i
$11$	0.147235	−	0.255018i	0.0443930	−	0.0768909i	−0.842975	−	0.537953i	$-0.819198\pi$
$11$	0.147235	−	0.255018i	0.0443930	−	0.0768909i	0.887368	+	0.461062i	$0.152531\pi$
$12$	−2.05004	+	2.79237i	−0.591795	+	0.806088i
$13$	−1.99299	−	3.45197i	−0.552757	−	0.957404i	−0.998074	−	0.0620307i	$-0.980242\pi$
$13$	−1.99299	−	3.45197i	−0.552757	−	0.957404i	0.445317	−	0.895373i	$-0.353091\pi$
$14$	−0.909846	+	1.08267i	−0.243167	+	0.289356i
$15$	1.56769	+	6.38203i	0.404775	+	1.64783i
$16$	3.05650	+	2.58028i	0.764124	+	0.645069i
$17$		−	3.60857i		−	0.875207i	−0.899168	−	0.437603i	$-0.855827\pi$
$17$		−	3.60857i		−	0.875207i	0.899168	−	0.437603i	$-0.144173\pi$
$18$	−2.86306	+	3.13096i	−0.674829	+	0.737974i
$19$		−	6.02570i		−	1.38239i	−0.722668	−	0.691195i	$-0.757085\pi$
$19$		−	6.02570i		−	1.38239i	0.722668	−	0.691195i	$-0.242915\pi$
$20$	7.47508	−	1.30657i	1.67148	−	0.292158i
$21$	−1.25011	+	1.19885i	−0.272795	+	0.261610i
$22$	−0.318814	−	0.267922i	−0.0679715	−	0.0571212i
$23$	2.37532	+	4.11418i	0.495289	+	0.857865i	0.999985	−	0.00543156i	$-0.00172893\pi$
$23$	2.37532	+	4.11418i	0.495289	+	0.857865i	−0.504696	+	0.863297i	$0.668396\pi$
$24$	3.38294	+	3.54341i	0.690539	+	0.723295i
$25$	4.69800	−	8.13717i	0.939600	−	1.62743i
$26$	−5.29852	+	1.92403i	−1.03913	+	0.377334i
$27$	−3.89752	+	3.43647i	−0.750079	+	0.661348i
$28$	1.28329	+	1.53400i	0.242519	+	0.289900i
$29$	0.904457	+	0.522189i	0.167954	+	0.0969680i	0.581621	−	0.813460i	$-0.302419\pi$
$29$	0.904457	+	0.522189i	0.167954	+	0.0969680i	−0.413667	+	0.910428i	$0.635752\pi$
$30$	9.27388	−	0.609178i	1.69317	−	0.111220i
$31$	5.56802	−	3.21470i	1.00005	−	0.577376i	0.0917836	−	0.995779i	$-0.470743\pi$
$31$	5.56802	−	3.21470i	1.00005	−	0.577376i	0.908262	+	0.418403i	$0.137410\pi$
$32$	4.34693	−	3.61998i	0.768435	−	0.639928i
$33$	−0.353025	−	0.368119i	−0.0614537	−	0.0640812i
$34$	−5.02510	−	0.889923i	−0.861797	−	0.152621i
$35$	3.79421			0.641338
$36$	3.65393	+	4.75907i	0.608989	+	0.793179i
$37$	−3.86636			−0.635626			−0.317813	−	0.948153i	$-0.602948\pi$
$37$	−3.86636			−0.635626			−0.317813	+	0.948153i	$0.602948\pi$
$38$	−8.39106	−	1.48602i	−1.36121	−	0.241064i
$39$	−6.70462	+	1.64693i	−1.07360	+	0.263720i
$40$	0.0240018	−	10.7316i	0.00379502	−	1.69682i
$41$	−10.6945	+	6.17450i	−1.67021	+	0.964295i	−0.702687	+	0.711499i	$0.748017\pi$
$41$	−10.6945	+	6.17450i	−1.67021	+	0.964295i	−0.967520	+	0.252796i	$0.918650\pi$
$42$	1.36116	+	2.03648i	0.210031	+	0.314236i
$43$	−0.852502	−	0.492192i	−0.130005	−	0.0750586i	0.433587	−	0.901112i	$-0.357248\pi$
$43$	−0.852502	−	0.492192i	−0.130005	−	0.0750586i	−0.563592	+	0.826053i	$0.690581\pi$
$44$	−0.451718	+	0.377890i	−0.0680991	+	0.0569691i
$45$	11.3726	+	0.476285i	1.69533	+	0.0710004i
$46$	6.31496	−	2.29313i	0.931091	−	0.338103i
$47$	1.68371	−	2.91626i	0.245594	−	0.425381i	−0.716705	−	0.697377i	$-0.754350\pi$
$47$	1.68371	−	2.91626i	0.245594	−	0.425381i	0.962298	+	0.271996i	$0.0876838\pi$
$48$	5.76863	−	3.83704i	0.832631	−	0.553829i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−10.1728	−	8.54892i	−1.43865	−	1.20900i
$51$	−6.00208	−	1.74366i	−0.840460	−	0.244161i
$52$	1.37261	+	7.85292i	0.190347	+	1.08900i
$53$		−	2.03029i		−	0.278882i	−0.990230	−	0.139441i	$-0.955469\pi$
$53$		−	2.03029i		−	0.278882i	0.990230	−	0.139441i	$-0.0445306\pi$
$54$	3.82425	+	6.27496i	0.520415	+	0.853914i
$55$			1.11728i			0.150654i
$56$	2.45265	−	1.40873i	0.327749	−	0.188250i
$57$	−10.0225	−	2.91162i	−1.32751	−	0.385653i
$58$	0.950223	−	1.13072i	0.124770	−	0.148471i
$59$	−4.15275	−	7.19278i	−0.540642	−	0.936420i	−0.998867	−	0.0475837i	$-0.984848\pi$
$59$	−4.15275	−	7.19278i	−0.540642	−	0.936420i	0.458225	−	0.888836i	$-0.348485\pi$
$60$	1.43876	−	13.0645i	0.185743	−	1.68662i
$61$	−5.48589	+	9.50184i	−0.702397	+	1.21659i	0.265226	+	0.964186i	$0.414553\pi$
$61$	−5.48589	+	9.50184i	−0.702397	+	1.21659i	−0.967623	+	0.252400i	$0.918780\pi$
$62$	−3.10346	−	8.54650i	−0.394140	−	1.08541i
$63$	1.38997	+	2.65857i	0.175120	+	0.334948i
$64$	−3.96897	−	6.94603i	−0.496121	−	0.868253i
$65$	13.0975	+	7.56183i	1.62454	+	0.937930i
$66$	−0.599682	+	0.400819i	−0.0738158	+	0.0493375i
$67$	9.26153	−	5.34715i	1.13148	−	0.653258i	0.187170	−	0.982327i	$-0.440068\pi$
$67$	9.26153	−	5.34715i	1.13148	−	0.653258i	0.944306	+	0.329069i	$0.106735\pi$
$68$	−2.47852	+	6.77821i	−0.300564	+	0.821978i
$69$	7.99081	−	1.96287i	0.961980	−	0.236302i
$70$	0.935704	−	5.28360i	0.111838	−	0.631511i
$71$	2.73284			0.324329			0.162164	−	0.986764i	$-0.448152\pi$
$71$	2.73284			0.324329			0.162164	+	0.986764i	$0.448152\pi$
$72$	7.52833	−	3.91461i	0.887223	−	0.461342i
$73$	8.63292			1.01041			0.505203	−	0.863000i	$-0.331417\pi$
$73$	8.63292			1.01041			0.505203	+	0.863000i	$0.331417\pi$
$74$	−0.953498	+	5.38408i	−0.110842	+	0.625886i
$75$	−11.2644	−	11.7460i	−1.30070	−	1.35631i
$76$	−4.13870	+	11.3185i	−0.474742	+	1.29832i
$77$	−0.255018	+	0.147235i	−0.0290620	+	0.0167790i
$78$	0.639970	+	9.74264i	0.0724623	+	1.10314i
$79$	4.74756	+	2.74100i	0.534142	+	0.308387i	0.742701	−	0.669623i	$-0.233544\pi$
$79$	4.74756	+	2.74100i	0.534142	+	0.308387i	−0.208560	+	0.978010i	$0.566878\pi$
$80$	−14.9383	−	2.67999i	−1.67016	−	0.299632i
$81$	3.83254	+	8.14319i	0.425838	+	0.904799i
$82$	5.96084	+	16.4153i	0.658265	+	1.81277i
$83$	4.07096	−	7.05111i	0.446846	−	0.773960i	−0.551333	−	0.834286i	$-0.685880\pi$
$83$	4.07096	−	7.05111i	0.446846	−	0.773960i	0.998179	+	0.0603253i	$0.0192138\pi$
$84$	3.17157	−	1.39325i	0.346047	−	0.152016i
$85$	6.84583	+	11.8573i	0.742534	+	1.28611i
$86$	−0.895639	+	1.06577i	−0.0965792	+	0.114925i
$87$	1.30558	−	1.25205i	0.139973	−	0.134234i
$88$	0.414829	+	0.722231i	0.0442209	+	0.0769900i
$89$		−	3.35572i		−	0.355706i	−0.984057	−	0.177853i	$-0.943085\pi$
$89$		−	3.35572i		−	0.355706i	0.984057	−	0.177853i	$-0.0569151\pi$
$90$	3.46790	−	15.7195i	0.365549	−	1.65698i
$91$			3.98599i			0.417845i
$92$	−1.63593	−	9.35939i	−0.170557	−	0.975784i
$93$	−2.65649	−	10.8145i	−0.275465	−	1.12142i
$94$	−3.64580	−	3.06383i	−0.376036	−	0.316010i
$95$	11.4314	+	19.7997i	1.17283	+	2.03141i
$96$	−3.92062	−	8.97935i	−0.400147	−	0.916451i
$97$	6.74076	−	11.6753i	0.684421	−	1.18545i	−0.289198	−	0.957269i	$-0.593389\pi$
$97$	6.74076	−	11.6753i	0.684421	−	1.18545i	0.973619	−	0.228182i	$-0.0732781\pi$
$98$	1.32929	−	0.482699i	0.134278	−	0.0487599i
$99$	−0.782868	+	0.409306i	−0.0786811	+	0.0411368i
$100$	−14.4135	+	12.0578i	−1.44135	+	1.20578i
$101$	−11.1419	−	6.43278i	−1.10866	−	0.640085i	−0.170178	−	0.985413i	$-0.554434\pi$
$101$	−11.1419	−	6.43278i	−1.10866	−	0.640085i	−0.938482	+	0.345328i	$0.887768\pi$
$102$	−3.90832	+	7.92816i	−0.386981	+	0.785005i
$103$	−7.71860	+	4.45634i	−0.760537	+	0.439096i	−0.829488	−	0.558524i	$-0.811368\pi$
$103$	−7.71860	+	4.45634i	−0.760537	+	0.439096i	0.0689517	+	0.997620i	$0.478035\pi$
$104$	11.2741	+	0.0252150i	1.10551	+	0.00247254i
$105$	1.83336	−	6.31085i	0.178918	−	0.615876i
$106$	−2.82728	−	0.500699i	−0.274609	−	0.0486322i
$107$	−2.28113			−0.220525			−0.110263	−	0.993902i	$-0.535169\pi$
$107$	−2.28113			−0.220525			−0.110263	+	0.993902i	$0.535169\pi$
$108$	9.68127	−	3.77795i	0.931581	−	0.363534i
$109$	−10.0544			−0.963032			−0.481516	−	0.876437i	$-0.659914\pi$
$109$	−10.0544			−0.963032			−0.481516	+	0.876437i	$0.659914\pi$
$110$	1.55586	+	0.275537i	0.148346	+	0.0262714i
$111$	−1.86822	+	6.43086i	−0.177324	+	0.610390i
$112$	−1.35687	−	3.76283i	−0.128212	−	0.355554i
$113$	6.07706	−	3.50859i	0.571682	−	0.330061i	−0.186139	−	0.982523i	$-0.559597\pi$
$113$	6.07706	−	3.50859i	0.571682	−	0.330061i	0.757821	+	0.652463i	$0.226264\pi$
$114$	−6.52623	+	13.2387i	−0.611238	+	1.23992i
$115$	−15.6100	−	9.01246i	−1.45564	−	0.840416i
$116$	−1.34024	−	1.60208i	−0.124438	−	0.148749i
$117$	−0.500359	+	11.9475i	−0.0462582	+	1.10455i
$118$	−11.0404	+	4.00906i	−1.01635	+	0.369064i
$119$	−1.80429	+	3.12511i	−0.165399	+	0.286479i
$120$	−17.8381	−	5.22543i	−1.62839	−	0.477015i
$121$	5.45664	+	9.45118i	0.496059	+	0.859199i
$122$	11.8788	+	9.98264i	1.07546	+	0.903786i
$123$	5.10235	+	20.7716i	0.460063	+	1.87291i
$124$	−12.6667	+	2.21402i	−1.13751	+	0.198825i
$125$			16.6793i			1.49184i
$126$	4.04496	−	1.27996i	0.360354	−	0.114028i
$127$		−	6.98999i		−	0.620262i	−0.950694	−	0.310131i	$-0.899627\pi$
$127$		−	6.98999i		−	0.620262i	0.950694	−	0.310131i	$-0.100373\pi$
$128$	−10.6515	+	3.81398i	−0.941465	+	0.337112i
$129$	−1.23059	+	1.18013i	−0.108347	+	0.103904i
$130$	13.7602	−	16.3740i	1.20685	−	1.43609i
$131$	5.94819	+	10.3026i	0.519696	+	0.900139i	0.999738	+	0.0228940i	$0.00728803\pi$
$131$	5.94819	+	10.3026i	0.519696	+	0.900139i	−0.480042	+	0.877245i	$0.659379\pi$
$132$	0.410269	+	0.933932i	0.0357093	+	0.0812884i
$133$	−3.01285	+	5.21841i	−0.261247	+	0.452493i
$134$	−5.16212	−	14.2158i	−0.445939	−	1.22806i
$135$	6.28746	−	18.6858i	0.541138	−	1.60822i
$136$	8.82772	+	5.12305i	0.756971	+	0.439297i
$137$	−0.240419	−	0.138806i	−0.0205404	−	0.0118590i	0.489695	−	0.871894i	$-0.337108\pi$
$137$	−0.240419	−	0.138806i	−0.0205404	−	0.0118590i	−0.510235	+	0.860035i	$0.670442\pi$
$138$	−0.762739	−	11.6116i	−0.0649286	−	0.988447i
$139$	−9.51784	+	5.49513i	−0.807293	+	0.466091i	−0.846015	−	0.533159i	$-0.821005\pi$
$139$	−9.51784	+	5.49513i	−0.807293	+	0.466091i	0.0387220	+	0.999250i	$0.487671\pi$
$140$	−7.12690	−	2.60602i	−0.602333	−	0.220249i
$141$	−4.03701	−	4.20962i	−0.339978	−	0.354514i
$142$	0.673957	−	3.80561i	0.0565572	−	0.319360i
$143$	−1.17375			−0.0981542
$144$	−3.59469	−	11.4489i	−0.299557	−	0.954078i
$145$	−3.96258			−0.329075
$146$	2.12900	−	12.0217i	0.176197	−	0.994925i
$147$	1.68205	−	0.413179i	0.138733	−	0.0340785i
$148$	7.26243	+	2.65558i	0.596968	+	0.218287i
$149$	7.22393	−	4.17074i	0.591808	−	0.341680i	−0.174004	−	0.984745i	$-0.555671\pi$
$149$	7.22393	−	4.17074i	0.591808	−	0.341680i	0.765812	+	0.643065i	$0.222337\pi$
$150$	−19.1348	+	12.7894i	−1.56235	+	1.04425i
$151$	4.58601	+	2.64773i	0.373204	+	0.215469i	0.674857	−	0.737948i	$-0.264205\pi$
$151$	4.58601	+	2.64773i	0.373204	+	0.215469i	−0.301653	+	0.953418i	$0.597539\pi$
$152$	14.7408	+	8.55462i	1.19564	+	0.693871i
$153$	−5.80041	+	9.14064i	−0.468935	+	0.738977i
$154$	0.142140	+	0.391435i	0.0114540	+	0.0315427i
$155$	−12.1972	+	21.1262i	−0.979704	+	1.69690i
$156$	13.7249	+	1.51148i	1.09887	+	0.121016i
$157$	4.66952	+	8.08784i	0.372668	+	0.645480i	0.989975	−	0.141242i	$-0.0451097\pi$
$157$	4.66952	+	8.08784i	0.372668	+	0.645480i	−0.617307	+	0.786722i	$0.711776\pi$
$158$	4.98778	−	5.93522i	0.396807	−	0.472180i
$159$	−3.37696	−	0.981038i	−0.267810	−	0.0778014i
$160$	−7.41600	+	20.1414i	−0.586286	+	1.59232i
$161$		−	4.75064i		−	0.374403i
$162$	12.2849	−	3.32876i	0.965195	−	0.261532i
$163$		−	15.6620i		−	1.22674i	−0.789794	−	0.613372i	$-0.789813\pi$
$163$		−	15.6620i		−	1.22674i	0.789794	−	0.613372i	$-0.210187\pi$
$164$	24.3291	−	4.25249i	1.89979	−	0.332064i
$165$	1.85835	+	0.539869i	0.144673	+	0.0420288i
$166$	−8.81504	−	7.40790i	−0.684179	−	0.574965i
$167$	1.43448	+	2.48460i	0.111004	+	0.192264i	0.916175	−	0.400778i	$-0.131260\pi$
$167$	1.43448	+	2.48460i	0.111004	+	0.192264i	−0.805172	+	0.593042i	$0.797927\pi$
$168$	−1.15800	−	4.76015i	−0.0893420	−	0.367254i
$169$	−1.44406	+	2.50118i	−0.111081	+	0.192398i
$170$	18.2001	−	6.60895i	1.39589	−	0.506883i
$171$	−9.68570	+	15.2633i	−0.740684	+	1.16721i
$172$	1.26325	+	1.51005i	0.0963219	+	0.115140i
$173$	5.95609	+	3.43875i	0.452833	+	0.261443i	0.709026	−	0.705182i	$-0.249135\pi$
$173$	5.95609	+	3.43875i	0.452833	+	0.261443i	−0.256193	+	0.966626i	$0.582468\pi$
$174$	−1.42156	−	2.12686i	−0.107768	−	0.161236i
$175$	−8.13717	+	4.69800i	−0.615113	+	0.355135i
$176$	1.10804	−	0.399556i	0.0835217	−	0.0301177i
$177$	−13.9703	+	3.43166i	−1.05007	+	0.257940i
$178$	−4.67299	−	0.827567i	−0.350255	−	0.0620288i
$179$	−19.3475			−1.44610			−0.723050	−	0.690796i	$-0.757260\pi$
$179$	−19.3475			−1.44610			−0.723050	+	0.690796i	$0.757260\pi$
$180$	−21.0348	−	8.70585i	−1.56784	−	0.648895i
$181$	−12.6872			−0.943032			−0.471516	−	0.881858i	$-0.656293\pi$
$181$	−12.6872			−0.943032			−0.471516	+	0.881858i	$0.656293\pi$
$182$	5.55067	+	0.983000i	0.411443	+	0.0728648i
$183$	13.1535	+	13.7159i	0.972334	+	1.01391i
$184$	−13.4368	−	0.0300522i	−0.990575	−	0.00221547i
$185$	12.7044	−	7.33488i	0.934045	−	0.539271i
$186$	−15.7149	+	1.03227i	−1.15227	+	0.0756897i
$187$	−0.920252	−	0.531308i	−0.0672955	−	0.0388531i
$188$	−5.16562	+	4.32136i	−0.376742	+	0.315168i
$189$	5.09359	−	1.02731i	0.370504	−	0.0747255i
$190$	30.3911	−	11.0358i	2.20480	−	0.800622i
$191$	4.15917	−	7.20389i	0.300947	−	0.521255i	−0.675404	−	0.737448i	$-0.736031\pi$
$191$	4.15917	−	7.20389i	0.300947	−	0.521255i	0.976351	+	0.216193i	$0.0693640\pi$
$192$	−13.4710	+	3.24521i	−0.972188	+	0.234203i
$193$	5.39565	+	9.34554i	0.388387	+	0.672707i	0.992233	−	0.124395i	$-0.0396989\pi$
$193$	5.39565	+	9.34554i	0.388387	+	0.672707i	−0.603845	+	0.797101i	$0.706366\pi$
$194$	−14.5961	−	12.2661i	−1.04794	−	0.880656i
$195$	18.9062	−	18.1310i	1.35390	−	1.29839i
$196$	−0.344359	−	1.97013i	−0.0245971	−	0.140724i
$197$		−	14.3939i		−	1.02553i	−0.858530	−	0.512763i	$-0.828622\pi$
$197$		−	14.3939i		−	1.02553i	0.858530	−	0.512763i	$-0.171378\pi$
$198$	0.376911	+	1.19112i	0.0267859	+	0.0846491i
$199$		−	14.9925i		−	1.06279i	−0.847124	−	0.531395i	$-0.821668\pi$
$199$		−	14.9925i		−	1.06279i	0.847124	−	0.531395i	$-0.178332\pi$
$200$	13.2364	+	23.0451i	0.935958	+	1.62953i
$201$	−4.41866	−	17.9883i	−0.311668	−	1.26880i
$202$	−11.7057	+	13.9292i	−0.823609	+	0.980054i
$203$	−0.522189	−	0.904457i	−0.0366505	−	0.0634805i
$204$	10.0765	+	7.39771i	0.705494	+	0.517943i
$205$	23.4273	−	40.5773i	1.63623	−	2.83404i
$206$	4.30214	+	11.8475i	0.299744	+	0.825454i
$207$	0.596346	−	14.2394i	0.0414489	−	0.989710i
$208$	2.81545	−	15.6934i	0.195216	−	1.08814i
$209$	−1.53666	−	0.887194i	−0.106293	−	0.0613685i
$210$	−8.33601	−	4.10938i	−0.575239	−	0.283574i
$211$	2.48466	−	1.43452i	0.171051	−	0.0987564i	−0.412030	−	0.911170i	$-0.635180\pi$
$211$	2.48466	−	1.43452i	0.171051	−	0.0987564i	0.583081	+	0.812414i	$0.301847\pi$
$212$	−1.39449	+	3.81363i	−0.0957740	+	0.261921i
$213$	1.32051	−	4.54550i	0.0904798	−	0.311452i
$214$	−0.562559	+	3.17658i	−0.0384557	+	0.217147i
$215$	3.73496			0.254722
$216$	−2.87343	−	14.4133i	−0.195512	−	0.980701i
$217$	−6.42939			−0.436456
$218$	−2.47954	+	14.0011i	−0.167936	+	0.948277i
$219$	4.17142	−	14.3590i	0.281879	−	0.970292i
$220$	0.767394	−	2.09866i	0.0517377	−	0.141491i
$221$	−12.4567	+	7.19186i	−0.837926	+	0.483777i
$222$	8.49453	+	4.18752i	0.570116	+	0.281048i
$223$	14.5462	+	8.39828i	0.974088	+	0.562390i	0.900480	−	0.434897i	$-0.143215\pi$
$223$	14.5462	+	8.39828i	0.974088	+	0.562390i	0.0736082	+	0.997287i	$0.476549\pi$
$224$	−5.57454	+	0.961530i	−0.372464	+	0.0642449i
$225$	−24.9799	+	13.0602i	−1.66533	+	0.870680i
$226$	−3.38719	−	9.32785i	−0.225312	−	0.620479i
$227$	14.3890	−	24.9225i	0.955033	−	1.65417i	0.220742	−	0.975332i	$-0.429152\pi$
$227$	14.3890	−	24.9225i	0.955033	−	1.65417i	0.734291	−	0.678834i	$-0.237515\pi$
$228$	16.8260	+	12.3529i	1.11433	+	0.818092i
$229$	−9.30663	−	16.1196i	−0.614999	−	1.06521i	−0.990385	−	0.138341i	$-0.955823\pi$
$229$	−9.30663	−	16.1196i	−0.614999	−	1.06521i	0.375385	−	0.926869i	$-0.377510\pi$
$230$	−16.3999	+	19.5151i	−1.08138	+	1.28679i
$231$	0.121669	+	0.495312i	0.00800523	+	0.0325892i
$232$	−2.56149	+	1.47125i	−0.168170	+	0.0965921i
$233$			25.3473i			1.66056i	0.557348	+	0.830279i	$0.311819\pi$
$233$			25.3473i			1.66056i	−0.557348	+	0.830279i	$0.688181\pi$
$234$	16.5140	+	3.64319i	1.07956	+	0.238163i
$235$			12.7767i			0.833457i
$236$	2.86008	+	16.3629i	0.186175	+	1.06514i
$237$	6.85309	−	6.57209i	0.445156	−	0.426903i
$238$	3.90690	+	3.28324i	0.253247	+	0.212821i
$239$	−12.5884	−	21.8038i	−0.814279	−	1.41037i	−0.909845	−	0.414949i	$-0.863799\pi$
$239$	−12.5884	−	21.8038i	−0.814279	−	1.41037i	0.0955656	−	0.995423i	$-0.469534\pi$
$240$	−11.6758	+	23.5517i	−0.753668	+	1.52026i
$241$	−4.83687	+	8.37771i	−0.311570	+	0.539656i	−0.978703	−	0.205284i	$-0.934188\pi$
$241$	−4.83687	+	8.37771i	−0.311570	+	0.539656i	0.667132	+	0.744939i	$0.267522\pi$
$242$	14.5069	−	5.26783i	0.932538	−	0.338629i
$243$	15.3963	−	2.43982i	0.987676	−	0.156515i
$244$	16.8308	−	14.0800i	1.07748	−	0.901378i
$245$	−3.28588	−	1.89710i	−0.209927	−	0.121201i
$246$	30.1837	−	1.98269i	1.92444	−	0.126412i
$247$	−20.8005	+	12.0092i	−1.32351	+	0.764126i
$248$	−0.0406718	+	18.1850i	−0.00258266	+	1.15475i
$249$	−9.76092	−	10.1783i	−0.618573	−	0.645021i
$250$	23.2267	+	4.11335i	1.46899	+	0.260151i
$251$	9.27090			0.585174			0.292587	−	0.956239i	$-0.405484\pi$
$251$	9.27090			0.585174			0.292587	+	0.956239i	$0.405484\pi$
$252$	−0.784863	−	5.94844i	−0.0494417	−	0.374717i
$253$	1.39892			0.0879494
$254$	−9.73388	−	1.72383i	−0.610758	−	0.108163i
$255$	23.0300	−	5.65711i	1.44220	−	0.354262i
$256$	2.68435	+	15.7732i	0.167772	+	0.985826i
$257$	12.1695	−	7.02607i	0.759113	−	0.438274i	−0.0698640	−	0.997557i	$-0.522257\pi$
$257$	12.1695	−	7.02607i	0.759113	−	0.438274i	0.828977	+	0.559282i	$0.188923\pi$
$258$	1.33990	+	2.00468i	0.0834186	+	0.124806i
$259$	3.34837	+	1.93318i	0.208057	+	0.120122i
$260$	−19.4080	−	23.1998i	−1.20364	−	1.43879i
$261$	−1.45166	−	2.77655i	−0.0898554	−	0.171864i
$262$	15.8137	−	5.74237i	0.976973	−	0.354765i
$263$	3.96550	−	6.86845i	0.244523	−	0.423527i	−0.717474	−	0.696585i	$-0.754702\pi$
$263$	3.96550	−	6.86845i	0.244523	−	0.423527i	0.961997	+	0.273058i	$0.0880352\pi$
$264$	1.40172	−	0.340997i	0.0862700	−	0.0209869i
$265$	3.85168	+	6.67130i	0.236607	+	0.409815i
$266$	6.52386	+	5.48246i	0.400003	+	0.336151i
$267$	−5.58152	−	1.62148i	−0.341583	−	0.0992331i
$268$	−21.0692	+	3.68268i	−1.28700	+	0.224955i
$269$			6.36470i			0.388062i	0.980995	+	0.194031i	$0.0621563\pi$
$269$			6.36470i			0.388062i	−0.980995	+	0.194031i	$0.937844\pi$
$270$	−24.4703	−	13.3638i	−1.48921	−	0.813292i
$271$			2.98241i			0.181169i	0.995889	+	0.0905844i	$0.0288735\pi$
$271$			2.98241i			0.181169i	−0.995889	+	0.0905844i	$0.971127\pi$
$272$	9.31111	−	11.0296i	0.564569	−	0.668767i
$273$	6.62984	+	1.92603i	0.401256	+	0.116569i
$274$	−0.252584	+	0.300563i	−0.0152592	+	0.0181577i
$275$	−1.38342	−	2.39615i	−0.0834233	−	0.144493i
$276$	−16.3578	−	1.80144i	−0.984625	−	0.108434i
$277$	−10.7876	+	18.6847i	−0.648164	+	1.12265i	0.335397	+	0.942077i	$0.391130\pi$
$277$	−10.7876	+	18.6847i	−0.648164	+	1.12265i	−0.983561	+	0.180576i	$0.942204\pi$
$278$	5.30498	+	14.6092i	0.318172	+	0.876202i
$279$	−19.2713	−	0.807078i	−1.15374	−	0.0483185i
$280$	−5.38659	+	9.28184i	−0.321910	+	0.554696i
$281$	−7.00028	−	4.04161i	−0.417602	−	0.241103i	0.276449	−	0.961029i	$-0.410842\pi$
$281$	−7.00028	−	4.04161i	−0.417602	−	0.241103i	−0.694051	+	0.719926i	$0.744176\pi$
$282$	−6.85767	+	4.58357i	−0.408368	+	0.272948i
$283$	−0.719769	+	0.415559i	−0.0427858	+	0.0247024i	−0.521240	−	0.853410i	$-0.674530\pi$
$283$	−0.719769	+	0.415559i	−0.0427858	+	0.0247024i	0.478455	+	0.878112i	$0.341197\pi$
$284$	−5.13327	−	1.87703i	−0.304604	−	0.111381i
$285$	38.4562	−	9.44642i	2.27795	−	0.559557i
$286$	−0.289464	+	1.63451i	−0.0171164	+	0.0966503i
$287$	12.3490			0.728938
$288$	−16.8297	+	2.18229i	−0.991697	+	0.128593i
$289$	3.97822			0.234013
$290$	−0.977228	+	5.51808i	−0.0573848	+	0.324033i
$291$	−16.1623	−	16.8533i	−0.947450	−	0.987960i
$292$	−16.2158	−	5.92945i	−0.948956	−	0.346995i
$293$	11.2950	−	6.52120i	0.659864	−	0.380972i	−0.132361	−	0.991202i	$-0.542256\pi$
$293$	11.2950	−	6.52120i	0.659864	−	0.380972i	0.792225	+	0.610229i	$0.208923\pi$
$294$	−0.160555	−	2.44422i	−0.00936375	−	0.142550i
$295$	27.2909	+	15.7564i	1.58894	+	0.917373i
$296$	5.48903	−	9.45835i	0.319043	−	0.549756i
$297$	0.302511	+	1.49991i	0.0175535	+	0.0870335i
$298$	−4.02642	−	11.0882i	−0.233244	−	0.642323i
$299$	9.46801	−	16.3991i	0.547549	−	0.948383i
$300$	13.0909	+	29.8001i	0.755806	+	1.72051i
$301$	0.492192	+	0.852502i	0.0283695	+	0.0491374i
$302$	4.81806	−	5.73325i	0.277248	−	0.329912i
$303$	−16.0833	+	15.4238i	−0.923962	+	0.886077i
$304$	15.5480	−	18.4175i	0.891737	−	1.05632i
$305$		−	41.6292i		−	2.38368i
$306$	11.2983	+	10.3315i	0.645880	+	0.590615i
$307$			32.6077i			1.86102i	0.366266	+	0.930510i	$0.380636\pi$
$307$			32.6077i			1.86102i	−0.366266	+	0.930510i	$0.619364\pi$
$308$	0.580144	−	0.101403i	0.0330568	−	0.00577800i
$309$	3.68253	+	14.9915i	0.209492	+	0.852839i
$310$	26.4112	+	22.1952i	1.50005	+	1.26060i
$311$	−6.47968	−	11.2231i	−0.367429	−	0.636406i	0.621734	−	0.783229i	$-0.286429\pi$
$311$	−6.47968	−	11.2231i	−0.367429	−	0.636406i	−0.989163	+	0.146823i	$0.953095\pi$
$312$	5.48956	−	18.7398i	0.310785	−	1.06093i
$313$	−3.72105	+	6.44505i	−0.210326	+	0.364296i	−0.951817	−	0.306668i	$-0.900786\pi$
$313$	−3.72105	+	6.44505i	−0.210326	+	0.364296i	0.741490	+	0.670963i	$0.234119\pi$
$314$	12.4142	−	4.50794i	0.700576	−	0.254398i
$315$	−9.61086	−	6.09880i	−0.541511	−	0.343628i
$316$	−7.03500	−	8.40942i	−0.395750	−	0.473067i
$317$	−0.272234	−	0.157175i	−0.0152902	−	0.00882780i	0.492335	−	0.870406i	$-0.336143\pi$
$317$	−0.272234	−	0.157175i	−0.0152902	−	0.00882780i	−0.507626	+	0.861578i	$0.669477\pi$
$318$	−2.19894	+	4.46063i	−0.123311	+	0.250140i
$319$	0.266336	−	0.153769i	0.0149119	−	0.00860940i
$320$	26.2189	+	15.2943i	1.46568	+	0.854975i
$321$	−1.10224	+	3.79417i	−0.0615212	+	0.211770i
$322$	−6.61548	−	1.17157i	−0.368667	−	0.0652893i
$323$	−21.7442			−1.20988
$324$	−1.60582	−	17.9282i	−0.0892123	−	0.996013i
$325$	−37.4524			−2.07748
$326$	−21.8101	−	3.86247i	−1.20795	−	0.213923i
$327$	−4.85826	+	16.7233i	−0.268662	+	0.924798i
$328$	0.0781187	−	34.9281i	0.00431338	−	1.92858i
$329$	−2.91626	+	1.68371i	−0.160779	+	0.0928257i
$330$	1.21009	−	2.45470i	0.0666132	−	0.135127i
$331$	18.2481	+	10.5356i	1.00301	+	0.579087i	0.909137	−	0.416497i	$-0.136742\pi$
$331$	18.2481	+	10.5356i	1.00301	+	0.579087i	0.0938717	+	0.995584i	$0.470076\pi$
$332$	−12.4897	+	10.4484i	−0.685464	+	0.573433i
$333$	9.79363	+	6.21478i	0.536687	+	0.340568i
$334$	3.81367	−	1.38484i	0.208675	−	0.0757753i
$335$	−20.2882	+	35.1402i	−1.10846	+	1.91991i
$336$	−6.91430	+	0.438654i	−0.377206	+	0.0239306i
$337$	−4.76860	−	8.25945i	−0.259762	−	0.449921i	0.706416	−	0.707797i	$-0.250311\pi$
$337$	−4.76860	−	8.25945i	−0.259762	−	0.449921i	−0.966178	+	0.257876i	$0.916977\pi$
$338$	3.12688	+	2.62774i	0.170080	+	0.142930i
$339$	−2.89936	−	11.8032i	−0.157471	−	0.641064i
$340$	−4.71485	−	26.9744i	−0.255699	−	1.46289i
$341$		−	1.89326i		−	0.102526i
$342$	18.8662	+	17.2519i	1.02017	+	0.932877i
$343$		−	1.00000i		−	0.0539949i
$344$	2.41435	−	1.38673i	0.130173	−	0.0747677i
$345$	−22.5331	+	21.6091i	−1.21314	+	1.16340i
$346$	6.25746	−	7.44608i	0.336403	−	0.400303i
$347$	−6.87336	−	11.9050i	−0.368981	−	0.639095i	0.620425	−	0.784266i	$-0.286960\pi$
$347$	−6.87336	−	11.9050i	−0.368981	−	0.639095i	−0.989407	+	0.145171i	$0.953627\pi$
$348$	−3.31232	+	1.45507i	−0.177559	+	0.0780002i
$349$	8.69604	−	15.0620i	0.465488	−	0.806249i	−0.533735	−	0.845652i	$-0.679212\pi$
$349$	8.69604	−	15.0620i	0.465488	−	0.806249i	0.999223	+	0.0394024i	$0.0125454\pi$
$350$	4.53544	+	12.4900i	0.242429	+	0.667617i
$351$	19.6303	+	6.60527i	1.04779	+	0.352563i
$352$	−0.283142	−	1.64153i	−0.0150915	−	0.0874940i
$353$	−16.2716	−	9.39439i	−0.866047	−	0.500013i	−1.46597e−5	−	1.00000i	$-0.500005\pi$
$353$	−16.2716	−	9.39439i	−0.866047	−	0.500013i	−0.866033	+	0.499987i	$0.833338\pi$
$354$	1.33349	+	20.3005i	0.0708741	+	1.07896i
$355$	−8.97979	+	5.18449i	−0.476598	+	0.275164i
$356$	−2.30485	+	6.30326i	−0.122157	+	0.334072i
$357$	4.32613	+	4.51109i	0.228963	+	0.238752i
$358$	−4.77136	+	26.9423i	−0.252174	+	1.42394i
$359$	−14.2512			−0.752151			−0.376076	−	0.926589i	$-0.622727\pi$
$359$	−14.2512			−0.752151			−0.376076	+	0.926589i	$0.622727\pi$
$360$	−17.3108	+	27.1450i	−0.912357	+	1.43067i
$361$	−17.3091			−0.911003
$362$	−3.12884	+	17.6675i	−0.164448	+	0.928582i
$363$	18.3567	−	4.50915i	0.963475	−	0.236669i
$364$	2.73774	−	7.48714i	0.143497	−	0.392433i
$365$	−28.3667	+	16.3775i	−1.48478	+	0.857240i
$366$	22.3438	−	14.9343i	1.16793	−	0.780629i
$367$	−1.87665	−	1.08348i	−0.0979604	−	0.0565574i	0.450219	−	0.892918i	$-0.351346\pi$
$367$	−1.87665	−	1.08348i	−0.0979604	−	0.0565574i	−0.548180	+	0.836360i	$0.684679\pi$
$368$	−3.35555	+	18.7040i	−0.174920	+	0.975011i
$369$	37.0145	+	1.55016i	1.92690	+	0.0806983i
$370$	−7.08107	−	19.5003i	−0.368128	−	1.01377i
$371$	−1.01515	+	1.75829i	−0.0527038	+	0.0912857i
$372$	−2.43802	+	22.1382i	−0.126405	+	1.14781i
$373$	−16.7324	−	28.9814i	−0.866370	−	1.50060i	−0.865680	−	0.500598i	$-0.833114\pi$
$373$	−16.7324	−	28.9814i	−0.866370	−	1.50060i	−0.000690393	−	1.00000i	$-0.500220\pi$
$374$	−0.966817	+	1.15046i	−0.0499929	+	0.0594891i
$375$	27.7425	+	8.05945i	1.43262	+	0.416188i
$376$	4.74378	+	8.25907i	0.244642	+	0.425929i
$377$		−	4.16288i		−	0.214399i
$378$	−0.174421	−	7.34640i	−0.00897122	−	0.377858i
$379$		−	6.82998i		−	0.350832i	−0.984494	−	0.175416i	$-0.943873\pi$
$379$		−	6.82998i		−	0.350832i	0.984494	−	0.175416i	$-0.0561271\pi$
$380$	−7.87300	−	45.0426i	−0.403876	−	2.31064i
$381$	−11.6264	−	3.37756i	−0.595636	−	0.173038i
$382$	−9.00603	−	7.56841i	−0.460789	−	0.387233i
$383$	−3.69911	−	6.40704i	−0.189016	−	0.327384i	0.755907	−	0.654679i	$-0.227196\pi$
$383$	−3.69911	−	6.40704i	−0.189016	−	0.327384i	−0.944922	+	0.327295i	$0.893863\pi$
$384$	1.19696	+	19.5593i	0.0610821	+	0.998133i
$385$	0.558640	−	0.967592i	0.0284709	−	0.0493131i
$386$	14.3447	−	5.20895i	0.730128	−	0.265128i
$387$	1.36827	+	2.61705i	0.0695531	+	0.133032i
$388$	−20.6807	+	17.3007i	−1.04990	+	0.878310i
$389$	15.0318	+	8.67863i	0.762144	+	0.440024i	0.830065	−	0.557667i	$-0.188303\pi$
$389$	15.0318	+	8.67863i	0.762144	+	0.440024i	−0.0679209	+	0.997691i	$0.521637\pi$
$390$	−20.5857	−	30.7991i	−1.04240	−	1.55957i
$391$	14.8463	−	8.57151i	0.750810	−	0.433480i
$392$	−2.82842	−	0.00632591i	−0.142857	−	0.000319507i
$393$	20.0103	−	4.91534i	1.00938	−	0.247946i
$394$	−20.0442	−	3.54975i	−1.00981	−	0.178834i
$395$	−20.7999			−1.04655
$396$	1.75164	−	0.231119i	0.0880231	−	0.0116141i
$397$	4.91004			0.246428			0.123214	−	0.992380i	$-0.460680\pi$
$397$	4.91004			0.246428			0.123214	+	0.992380i	$0.460680\pi$
$398$	−20.8777	−	3.69736i	−1.04651	−	0.185332i
$399$	7.22389	+	7.53276i	0.361647	+	0.377110i
$400$	35.3556	−	12.7491i	1.76778	−	0.637455i
$401$	−21.0371	+	12.1458i	−1.05054	+	0.606532i	−0.922802	−	0.385276i	$-0.874106\pi$
$401$	−21.0371	+	12.1458i	−1.05054	+	0.606532i	−0.127742	+	0.991807i	$0.540773\pi$
$402$	−26.1392	+	1.71702i	−1.30371	+	0.0856372i
$403$	−22.1941	−	12.8137i	−1.10556	−	0.638298i
$404$	16.5102	+	19.7358i	0.821415	+	0.981894i
$405$	−28.0418	−	19.4868i	−1.39341	−	0.968308i
$406$	−1.38828	+	0.504120i	−0.0688990	+	0.0250190i
$407$	−0.569263	+	0.985993i	−0.0282173	+	0.0488738i
$408$	12.7866	−	12.2076i	0.633033	−	0.604364i
$409$	19.1299	+	33.1340i	0.945915	+	1.63837i	0.753909	+	0.656979i	$0.228166\pi$
$409$	19.1299	+	33.1340i	0.945915	+	1.63837i	0.192006	+	0.981394i	$0.438501\pi$
$410$	−50.7282	−	42.6305i	−2.50529	−	2.10537i
$411$	−0.347045	+	0.332815i	−0.0171185	+	0.0164165i
$412$	17.5591	−	3.06916i	0.865077	−	0.151207i
$413$			8.30551i			0.408687i
$414$	−19.6820	−	4.34208i	−0.967318	−	0.213402i
$415$			30.8921i			1.51644i
$416$	−21.1594	−	7.79085i	−1.03743	−	0.381978i
$417$	4.54095	+	18.4861i	0.222371	+	0.905270i
$418$	−1.61442	+	1.92108i	−0.0789638	+	0.0939631i
$419$	−9.47453	−	16.4104i	−0.462861	−	0.801699i	0.536241	−	0.844065i	$-0.319844\pi$
$419$	−9.47453	−	16.4104i	−0.462861	−	0.801699i	−0.999102	+	0.0423659i	$0.986510\pi$
$420$	−7.77827	+	10.5948i	−0.379541	+	0.516975i
$421$	10.6034	−	18.3656i	0.516777	−	0.895084i	−0.483033	−	0.875602i	$-0.660465\pi$
$421$	10.6034	−	18.3656i	0.516777	−	0.895084i	0.999810	−	0.0194821i	$-0.00620175\pi$
$422$	−1.38488	−	3.81377i	−0.0674150	−	0.185652i
$423$	−8.95248	+	4.68062i	−0.435285	+	0.227579i
$424$	4.96675	+	2.88239i	0.241207	+	0.139981i
$425$	−29.3636	−	16.9531i	−1.42434	−	0.822344i
$426$	−6.00416	−	2.95985i	−0.290902	−	0.143405i
$427$	9.50184	−	5.48589i	0.459827	−	0.265481i
$428$	4.28480	+	1.56678i	0.207113	+	0.0757330i
$429$	−0.567158	+	1.95229i	−0.0273826	+	0.0942573i
$430$	0.921092	−	5.20110i	0.0444190	−	0.250819i
$431$	−6.24043			−0.300591			−0.150295	−	0.988641i	$-0.548023\pi$
$431$	−6.24043			−0.300591			−0.150295	+	0.988641i	$0.548023\pi$
$432$	−20.7798	+	0.446862i	−0.999769	+	0.0214996i
$433$	12.2312			0.587795			0.293897	−	0.955837i	$-0.405048\pi$
$433$	12.2312			0.587795			0.293897	+	0.955837i	$0.405048\pi$
$434$	−1.58558	+	8.95322i	−0.0761101	+	0.429768i
$435$	−1.91472	+	6.59091i	−0.0918038	+	0.316010i
$436$	18.8857	+	6.90575i	0.904462	+	0.330725i
$437$	24.7908	−	14.3130i	1.18590	−	0.684682i
$438$	−18.9668	−	9.35003i	−0.906271	−	0.446762i
$439$	17.4636	+	10.0826i	0.833492	+	0.481217i	0.855047	−	0.518551i	$-0.173528\pi$
$439$	17.4636	+	10.0826i	0.833492	+	0.481217i	−0.0215550	+	0.999768i	$0.506862\pi$
$440$	−2.73322	−	1.58619i	−0.130301	−	0.0756186i
$441$	0.125530	−	2.99737i	0.00597760	−	0.142732i
$442$	6.94300	+	19.1201i	0.330245	+	0.909450i
$443$	−14.2028	+	24.6000i	−0.674795	+	1.16878i	0.301733	+	0.953392i	$0.402435\pi$
$443$	−14.2028	+	24.6000i	−0.674795	+	1.16878i	−0.976529	+	0.215387i	$0.930899\pi$
$444$	7.92618	−	10.7963i	0.376160	−	0.512370i
$445$	6.36615	+	11.0265i	0.301784	+	0.522706i
$446$	15.2823	−	18.1852i	0.723637	−	0.861093i
$447$	−3.44653	−	14.0308i	−0.163015	−	0.663632i
$448$	−0.0357847	+	7.99992i	−0.00169067	+	0.377961i
$449$		−	8.88596i		−	0.419354i	−0.977771	−	0.209677i	$-0.932759\pi$
$449$		−	8.88596i		−	0.419354i	0.977771	−	0.209677i	$-0.0672413\pi$
$450$	12.0265	+	38.0064i	0.566936	+	1.79164i
$451$			3.63641i			0.171232i
$452$	−13.8248	+	2.41643i	−0.650263	+	0.113659i
$453$	6.61989	−	6.34845i	0.311030	−	0.298276i
$454$	−31.1572	−	26.1836i	−1.46228	−	1.22886i
$455$	−7.56183	−	13.0975i	−0.354504	−	0.614019i
$456$	21.3515	−	20.3846i	0.999876	−	0.954594i
$457$	5.43702	−	9.41720i	0.254333	−	0.440518i	−0.710381	−	0.703817i	$-0.751477\pi$
$457$	5.43702	−	9.41720i	0.254333	−	0.440518i	0.964714	+	0.263299i	$0.0848106\pi$
$458$	−24.7423	+	8.98459i	−1.15613	+	0.419822i
$459$	12.4007	+	14.0645i	0.578817	+	0.656474i
$460$	23.1312	+	27.6503i	1.07850	+	1.28920i
$461$	31.3246	+	18.0853i	1.45893	+	0.842316i	0.998959	−	0.0456166i	$-0.0145253\pi$
$461$	31.3246	+	18.0853i	1.45893	+	0.842316i	0.459974	+	0.887932i	$0.347859\pi$
$462$	0.719750	−	0.0472786i	0.0334858	−	0.00219960i
$463$	−7.50957	+	4.33565i	−0.348999	+	0.201495i	−0.664244	−	0.747516i	$-0.731247\pi$
$463$	−7.50957	+	4.33565i	−0.348999	+	0.201495i	0.315245	+	0.949010i	$0.397913\pi$
$464$	1.41708	+	3.92982i	0.0657863	+	0.182437i
$465$	29.2452	+	30.4956i	1.35621	+	1.41420i
$466$	35.2973	+	6.25100i	1.63511	+	0.289572i
$467$	13.4993			0.624671			0.312336	−	0.949972i	$-0.398889\pi$
$467$	13.4993			0.624671			0.312336	+	0.949972i	$0.398889\pi$
$468$	9.14590	−	22.0981i	0.422769	−	1.02148i
$469$	−10.6943			−0.493817
$470$	17.7921	+	3.15090i	0.820687	+	0.145340i
$471$	15.7087	−	3.85870i	0.723818	−	0.177799i
$472$	23.4915	+	0.0525399i	1.08128	+	0.00241835i
$473$	−0.251036	+	0.144936i	−0.0115427	+	0.00666416i
$474$	−7.46186	−	11.1640i	−0.342735	−	0.512779i
$475$	−49.0322	−	28.3087i	−2.24975	−	1.29889i
$476$	5.53556	−	4.63084i	0.253722	−	0.212254i
$477$	−3.26349	+	5.14281i	−0.149425	+	0.235473i
$478$	−33.4673	+	12.1529i	−1.53076	+	0.555859i
$479$	−19.1408	+	33.1529i	−0.874567	+	1.51480i	−0.0173444	+	0.999850i	$0.505521\pi$
$479$	−19.1408	+	33.1529i	−0.874567	+	1.51480i	−0.857223	+	0.514945i	$0.827812\pi$
$480$	29.9174	+	22.0672i	1.36554	+	1.00723i
$481$	7.70563	+	13.3465i	0.351347	+	0.608550i
$482$	10.4735	+	8.80163i	0.477055	+	0.400903i
$483$	−7.90167	−	2.29551i	−0.359539	−	0.104449i
$484$	−3.75809	−	21.5006i	−0.170822	−	0.977300i
$485$			51.1517i			2.32268i
$486$	0.399387	−	22.0418i	0.0181165	−	0.999836i
$487$		−	13.3113i		−	0.603193i	−0.953436	−	0.301597i	$-0.902480\pi$
$487$		−	13.3113i		−	0.603193i	0.953436	−	0.301597i	$-0.0975196\pi$
$488$	−15.4563	−	26.9099i	−0.699674	−	1.21815i
$489$	−26.0504	−	7.56789i	−1.17804	−	0.342232i
$490$	−3.45214	+	4.10788i	−0.155952	+	0.185575i
$491$	1.46735	+	2.54153i	0.0662207	+	0.114698i	0.897235	−	0.441554i	$-0.145573\pi$
$491$	1.46735	+	2.54153i	0.0662207	+	0.114698i	−0.831014	+	0.556251i	$0.812239\pi$
$492$	4.68273	−	42.5211i	0.211114	−	1.91700i
$493$	1.88435	−	3.26380i	0.0848671	−	0.146994i
$494$	11.5936	+	31.9273i	0.521622	+	1.43648i
$495$	1.79591	−	2.83011i	0.0807203	−	0.127204i
$496$	25.3134	+	4.54131i	1.13661	+	0.203911i
$497$	−2.36671	−	1.36642i	−0.106162	−	0.0612924i
$498$	−16.5809	+	11.0824i	−0.743007	+	0.496615i
$499$	32.3491	−	18.6768i	1.44815	−	0.836088i	0.449775	−	0.893142i	$-0.351504\pi$
$499$	32.3491	−	18.6768i	1.44815	−	0.836088i	0.998371	+	0.0570538i	$0.0181707\pi$
$500$	11.4561	−	31.3298i	0.512331	−	1.40111i
$501$	4.82573	−	1.18540i	0.215598	−	0.0529596i
$502$	2.28633	−	12.9101i	0.102044	−	0.576208i
$503$	29.1509			1.29978			0.649888	−	0.760030i	$-0.274816\pi$
$503$	29.1509			1.29978			0.649888	+	0.760030i	$0.274816\pi$
$504$	−8.47703	−	0.374011i	−0.377597	−	0.0166598i
$505$	48.8146			2.17222
$506$	0.344993	−	1.94806i	0.0153368	−	0.0866019i
$507$	3.46241	+	3.61045i	0.153771	+	0.160346i
$508$	−4.80102	+	13.1297i	−0.213011	+	0.582538i
$509$	−19.4308	+	11.2184i	−0.861255	+	0.497246i	−0.864432	−	0.502749i	$-0.832322\pi$
$509$	−19.4308	+	11.2184i	−0.861255	+	0.497246i	0.00317707	+	0.999995i	$0.498989\pi$
$510$	−2.19826	−	33.4655i	−0.0973407	−	1.48188i
$511$	−7.47633	−	4.31646i	−0.330733	−	0.190949i
$512$	22.6269	+	0.151821i	0.999977	+	0.00670960i
$513$	20.7071	+	23.4853i	0.914242	+	1.03690i
$514$	−6.78295	−	18.6793i	−0.299183	−	0.823909i
$515$	16.9083	−	29.2860i	0.745067	−	1.29049i
$516$	3.12205	−	1.37149i	0.137440	−	0.0603765i
$517$	−0.495801	−	0.858752i	−0.0218053	−	0.0377679i
$518$	3.51779	−	4.18600i	0.154563	−	0.183922i
$519$	8.59760	−	8.24507i	0.377393	−	0.361918i
$520$	−37.0930	+	21.3052i	−1.62664	+	0.934294i
$521$		−	19.1422i		−	0.838636i	−0.907839	−	0.419318i	$-0.862269\pi$
$521$		−	19.1422i		−	0.838636i	0.907839	−	0.419318i	$-0.137731\pi$
$522$	−4.22446	+	1.33676i	−0.184900	+	0.0585086i
$523$			7.09271i			0.310143i	0.987903	+	0.155071i	$0.0495607\pi$
$523$			7.09271i			0.310143i	−0.987903	+	0.155071i	$0.950439\pi$
$524$	−4.09663	−	23.4374i	−0.178962	−	1.02387i
$525$	3.88223	+	15.8045i	0.169435	+	0.689766i
$526$	−8.58668	−	7.21600i	−0.374397	−	0.314632i
$527$	−11.6005	−	20.0926i	−0.505324	−	0.875246i
$528$	−0.129171	−	2.03605i	−0.00562143	−	0.0886079i
$529$	0.215696	−	0.373597i	0.00937809	−	0.0162433i
$530$	10.2400	−	3.71840i	0.444796	−	0.161517i
$531$	−1.04259	+	24.8947i	−0.0452444	+	1.08034i
$532$	9.24345	−	7.73272i	0.400754	−	0.335256i
$533$	42.6283	+	24.6115i	1.84644	+	1.06604i
$534$	−3.63447	+	7.37264i	−0.157279	+	0.319045i
$535$	7.49553	−	4.32754i	0.324060	−	0.187096i
$536$	−0.0676512	+	30.2480i	−0.00292209	+	1.30651i
$537$	−9.34871	+	32.1804i	−0.403427	+	1.38869i
$538$	8.86313	+	1.56962i	0.382116	+	0.0676712i
$539$	0.294470			0.0126837
$540$	−24.6443	+	30.7803i	−1.06052	+	1.32457i
$541$	15.6391			0.672376			0.336188	−	0.941795i	$-0.390862\pi$
$541$	15.6391			0.672376			0.336188	+	0.941795i	$0.390862\pi$
$542$	4.15315	+	0.735505i	0.178393	+	0.0315926i
$543$	−6.13045	+	21.1024i	−0.263083	+	0.905592i
$544$	−13.0629	−	15.6862i	−0.560069	−	0.672540i
$545$	33.0374	−	19.0741i	1.41517	−	0.817047i
$546$	4.31709	−	8.75736i	0.184754	−	0.374781i
$547$	5.46377	+	3.15451i	0.233614	+	0.134877i	0.612238	−	0.790673i	$-0.290269\pi$
$547$	5.46377	+	3.15451i	0.233614	+	0.134877i	−0.378624	+	0.925551i	$0.623603\pi$
$548$	0.356257	+	0.425858i	0.0152185	+	0.0181918i
$549$	29.1692	−	15.2505i	1.24491	−	0.650876i
$550$	−3.67792	+	1.33555i	−0.156827	+	0.0569480i
$551$	3.14655	−	5.44999i	0.134048	−	0.232177i
$552$	−6.54265	+	22.3347i	−0.278474	+	0.950629i
$553$	−2.74100	−	4.74756i	−0.116559	−	0.201887i
$554$	23.3589	+	19.6301i	0.992424	+	0.834004i
$555$	−6.06124	−	24.6752i	−0.257285	−	1.04741i
$556$	21.6523	−	3.78460i	0.918260	−	0.160503i
$557$			22.2489i			0.942714i	0.881942	+	0.471357i	$0.156236\pi$
$557$			22.2489i			0.942714i	−0.881942	+	0.471357i	$0.843764\pi$
$558$	−5.87646	+	26.6371i	−0.248770	+	1.12764i
$559$			3.92375i			0.165957i
$560$	11.5970	+	9.79010i	0.490062	+	0.413707i
$561$	−1.32838	+	1.27391i	−0.0560843	+	0.0537847i
$562$	−7.35450	+	8.75149i	−0.310231	+	0.369159i
$563$	18.9723	+	32.8609i	0.799585	+	1.38492i	0.919887	+	0.392185i	$0.128281\pi$
$563$	18.9723	+	32.8609i	0.799585	+	1.38492i	−0.120301	+	0.992737i	$0.538386\pi$
$564$	4.69163	+	10.6800i	0.197553	+	0.449709i
$565$	−13.3123	+	23.0576i	−0.560054	+	0.970042i
$566$	0.401179	+	1.10479i	0.0168628	+	0.0464379i
$567$	0.752517	−	8.96848i	0.0316028	−	0.376641i
$568$	−3.87979	+	6.68541i	−0.162792	+	0.280514i
$569$	8.24731	+	4.76159i	0.345745	+	0.199616i	0.662810	−	0.748788i	$-0.269364\pi$
$569$	8.24731	+	4.76159i	0.345745	+	0.199616i	−0.317064	+	0.948404i	$0.602697\pi$
$570$	−3.67072	−	55.8816i	−0.153750	−	2.34062i
$571$	−21.0510	+	12.1538i	−0.880958	+	0.508621i	−0.870974	−	0.491329i	$-0.836511\pi$
$571$	−21.0510	+	12.1538i	−0.880958	+	0.508621i	−0.00998391	+	0.999950i	$0.503178\pi$
$572$	2.20474	+	0.806183i	0.0921847	+	0.0337082i
$573$	−9.97242	−	10.3988i	−0.416604	−	0.434416i
$574$	3.04543	−	17.1965i	0.127114	−	0.717769i
$575$	44.6370			1.86149
$576$	−1.11149	+	23.9742i	−0.0463119	+	0.998927i
$577$	−13.6033			−0.566311			−0.283156	−	0.959074i	$-0.591381\pi$
$577$	−13.6033			−0.566311			−0.283156	+	0.959074i	$0.591381\pi$
$578$	0.981085	−	5.53985i	0.0408077	−	0.230428i
$579$	18.1515	−	4.45874i	0.754350	−	0.185299i
$580$	7.44317	+	2.72167i	0.309061	+	0.113011i
$581$	−7.05111	+	4.07096i	−0.292529	+	0.168892i
$582$	−27.4549	+	18.3504i	−1.13804	+	0.760651i
$583$	−0.517763	−	0.298930i	−0.0214435	−	0.0123804i
$584$	−12.2561	+	21.1189i	−0.507159	+	0.873906i
$585$	−21.0215	−	40.2073i	−0.869132	−	1.66237i
$586$	−6.29555	−	17.3371i	−0.260067	−	0.716188i
$587$	3.27395	−	5.67065i	0.135130	−	0.234053i	−0.790517	−	0.612440i	$-0.790188\pi$
$587$	3.27395	−	5.67065i	0.135130	−	0.234053i	0.925647	+	0.378388i	$0.123521\pi$
$588$	−3.44328	−	0.379199i	−0.141999	−	0.0156379i
$589$	−19.3708	−	33.5512i	−0.798159	−	1.38245i
$590$	28.6718	−	34.1180i	1.18040	−	1.40462i
$591$	−23.9412	−	6.95515i	−0.984811	−	0.286097i
$592$	−11.8175	−	9.97628i	−0.485697	−	0.410022i
$593$		−	11.1137i		−	0.456386i	−0.973616	−	0.228193i	$-0.926718\pi$
$593$		−	11.1137i		−	0.456386i	0.973616	−	0.228193i	$-0.0732818\pi$
$594$	2.16329	−	0.0513616i	0.0887610	−	0.00210739i
$595$		−	13.6917i		−	0.561303i
$596$	−16.4338	+	2.87247i	−0.673155	+	0.117661i
$597$	−24.9368	−	7.24437i	−1.02060	−	0.296492i
$598$	−20.5015	−	17.2289i	−0.838369	−	0.704541i
$599$	−6.36905	−	11.0315i	−0.260232	−	0.450736i	0.706071	−	0.708141i	$-0.250466\pi$
$599$	−6.36905	−	11.0315i	−0.260232	−	0.450736i	−0.966304	+	0.257405i	$0.917132\pi$
$600$	44.7264	−	10.8806i	1.82595	−	0.444199i
$601$	−14.5547	+	25.2095i	−0.593699	+	1.02832i	0.400030	+	0.916502i	$0.369000\pi$
$601$	−14.5547	+	25.2095i	−0.593699	+	1.02832i	−0.993729	+	0.111815i	$0.964334\pi$
$602$	1.30853	−	0.475161i	0.0533317	−	0.0193661i
$603$	−32.0548	−	1.34245i	−1.30537	−	0.0546688i
$604$	−6.79561	−	8.12326i	−0.276510	−	0.330531i
$605$	−35.8597	−	20.7036i	−1.45791	−	0.841722i
$606$	17.5120	+	26.2005i	0.711377	+	1.06432i
$607$	−32.5285	+	18.7804i	−1.32029	+	0.762272i	−0.983775	−	0.179406i	$-0.942583\pi$
$607$	−32.5285	+	18.7804i	−1.32029	+	0.762272i	−0.336518	+	0.941677i	$0.609249\pi$
$608$	−21.8129	−	26.1933i	−0.884630	−	1.06228i
$609$	−1.75669	+	0.431515i	−0.0711848	+	0.0174859i
$610$	−57.9706	−	10.2663i	−2.34716	−	0.415672i
$611$	−13.4225			−0.543015
$612$	17.1734	−	13.1855i	0.694195	−	0.532991i
$613$	20.5622			0.830501			0.415250	−	0.909707i	$-0.363694\pi$
$613$	20.5622			0.830501			0.415250	+	0.909707i	$0.363694\pi$
$614$	45.4077	+	8.04151i	1.83251	+	0.324529i
$615$	−56.1716	−	58.5733i	−2.26506	−	2.36190i
$616$	0.00186279	−	0.832885i	7.50540e−5	−	0.0335579i
$617$	29.4852	−	17.0233i	1.18703	−	0.685333i	0.229400	−	0.973332i	$-0.426323\pi$
$617$	29.4852	−	17.0233i	1.18703	−	0.685333i	0.957631	+	0.288000i	$0.0929902\pi$
$618$	21.7846	−	1.43097i	0.876304	−	0.0575622i
$619$	32.9073	+	18.9990i	1.32265	+	0.763635i	0.984151	−	0.177330i	$-0.0567461\pi$
$619$	32.9073	+	18.9990i	1.32265	+	0.763635i	0.338503	+	0.940965i	$0.390079\pi$
$620$	37.4212	−	31.3051i	1.50287	−	1.25724i
$621$	−23.3961	−	7.87239i	−0.938853	−	0.315908i
$622$	−17.2267	+	6.25547i	−0.690728	+	0.250821i
$623$	−1.67786	+	2.90614i	−0.0672220	+	0.116432i
$624$	−24.7422	−	12.2659i	−0.990480	−	0.491031i
$625$	−8.15241	−	14.1204i	−0.326096	−	0.564815i
$626$	8.05736	+	6.77117i	0.322037	+	0.270630i
$627$	−2.21817	+	2.12722i	−0.0885852	+	0.0849530i
$628$	−3.21598	−	18.3991i	−0.128332	−	0.734205i
$629$			13.9520i			0.556304i
$630$	−10.8630	+	11.8795i	−0.432793	+	0.473291i
$631$		−	46.8749i		−	1.86606i	−0.359799	−	0.933030i	$-0.617155\pi$
$631$		−	46.8749i		−	1.86606i	0.359799	−	0.933030i	$-0.382845\pi$
$632$	−13.4454	+	7.72267i	−0.534830	+	0.307191i
$633$	−1.18543	−	4.82586i	−0.0471165	−	0.191811i
$634$	−0.286009	+	0.340337i	−0.0113589	+	0.0135165i
$635$	13.2607	+	22.9683i	0.526236	+	0.911468i
$636$	5.66934	+	4.16218i	0.224804	+	0.165041i
$637$	1.99299	−	3.45197i	0.0789653	−	0.136772i
$638$	−0.148448	−	0.408806i	−0.00587712	−	0.0161848i
$639$	−6.92239	−	4.39277i	−0.273846	−	0.173775i
$640$	27.7639	−	32.7392i	1.09746	−	1.29413i
$641$	−22.8062	−	13.1672i	−0.900792	−	0.520073i	−0.0233352	−	0.999728i	$-0.507429\pi$
$641$	−22.8062	−	13.1672i	−0.900792	−	0.520073i	−0.877457	+	0.479655i	$0.840762\pi$
$642$	5.01173	+	2.47062i	0.197797	+	0.0975075i
$643$	33.1788	−	19.1558i	1.30844	−	0.755430i	0.326608	−	0.945160i	$-0.394094\pi$
$643$	33.1788	−	19.1558i	1.30844	−	0.755430i	0.981836	+	0.189730i	$0.0607611\pi$
$644$	−3.26294	+	8.92343i	−0.128578	+	0.351633i
$645$	1.80473	−	6.21230i	0.0710612	−	0.244609i
$646$	−5.36241	+	30.2797i	−0.210981	+	1.19134i
$647$	31.8925			1.25382			0.626912	−	0.779090i	$-0.284318\pi$
$647$	31.8925			1.25382			0.626912	+	0.779090i	$0.284318\pi$
$648$	−25.3619	−	2.18517i	−0.996309	−	0.0858416i
$649$	−2.44572			−0.0960030
$650$	−9.23627	+	52.1541i	−0.362276	+	2.04565i
$651$	−3.10668	+	10.6939i	−0.121760	+	0.419127i
$652$	−10.7573	+	29.4190i	−0.421290	+	1.15214i
$653$	4.99048	−	2.88125i	0.195292	−	0.112752i	−0.399165	−	0.916879i	$-0.630700\pi$
$653$	4.99048	−	2.88125i	0.195292	−	0.112752i	0.594458	+	0.804127i	$0.297367\pi$
$654$	22.0898	+	10.8895i	0.863779	+	0.425815i
$655$	−39.0901	−	22.5687i	−1.52738	−	0.881830i
$656$	−48.6197	−	8.72255i	−1.89828	−	0.340558i
$657$	−21.8675	−	13.8765i	−0.853132	−	0.541375i
$658$	1.62545	+	4.47625i	0.0633664	+	0.174503i
$659$	−8.37638	+	14.5083i	−0.326298	+	0.565164i	−0.981774	−	0.190052i	$-0.939134\pi$
$659$	−8.37638	+	14.5083i	−0.326298	+	0.565164i	0.655477	+	0.755216i	$0.272468\pi$
$660$	−3.11986	−	2.29047i	−0.121440	−	0.0891563i
$661$	−8.26733	−	14.3194i	−0.321562	−	0.556961i	0.659249	−	0.751925i	$-0.270874\pi$
$661$	−8.26733	−	14.3194i	−0.321562	−	0.556961i	−0.980810	+	0.194964i	$0.937541\pi$
$662$	19.1715	−	22.8131i	0.745122	−	0.886658i
$663$	5.94306	+	24.1941i	0.230809	+	0.939621i
$664$	11.4698	+	19.9693i	0.445114	+	0.774958i
$665$		−	22.8627i		−	0.886579i
$666$	11.0696	−	12.1054i	0.428938	−	0.469075i
$667$			4.96146i			0.192109i
$668$	−0.987954	−	5.65223i	−0.0382251	−	0.218692i
$669$	20.9975	−	20.1365i	0.811809	−	0.778522i
$670$	43.9309	+	36.9183i	1.69720	+	1.42628i
$671$	1.61543	+	2.79801i	0.0623630	+	0.108016i
$672$	−1.09432	+	9.73666i	−0.0422142	+	0.375600i
$673$	−6.04519	+	10.4706i	−0.233025	+	0.403611i	−0.958697	−	0.284430i	$-0.908196\pi$
$673$	−6.04519	+	10.4706i	−0.233025	+	0.403611i	0.725672	+	0.688041i	$0.241529\pi$
$674$	−12.6777	+	4.60359i	−0.488325	+	0.177324i
$675$	9.65257	+	47.8594i	0.371527	+	1.84211i
$676$	4.43038	−	3.70628i	0.170399	−	0.142549i
$677$	−21.2204	−	12.2516i	−0.815567	−	0.470868i	0.0333185	−	0.999445i	$-0.489392\pi$
$677$	−21.2204	−	12.2516i	−0.815567	−	0.470868i	−0.848885	+	0.528577i	$0.822726\pi$
$678$	−17.1516	+	1.12664i	−0.658702	+	0.0432685i
$679$	−11.6753	+	6.74076i	−0.448058	+	0.258687i
$680$	−38.7258	−	0.0866122i	−1.48507	−	0.00332143i
$681$	−34.5005	−	35.9756i	−1.32206	−	1.37859i
$682$	−2.63645	−	0.466905i	−0.100955	−	0.0178787i
$683$	50.4915			1.93200			0.966002	−	0.258534i	$-0.0832394\pi$
$683$	50.4915			1.93200			0.966002	+	0.258534i	$0.0832394\pi$
$684$	28.6767	−	22.0175i	1.09648	−	0.841860i
$685$	1.05332			0.0402452
$686$	−1.39255	−	0.246614i	−0.0531676	−	0.00941576i
$687$	−31.3084	+	7.69061i	−1.19449	+	0.293415i
$688$	−1.33568	−	3.70408i	−0.0509222	−	0.141217i
$689$	−7.00851	+	4.04637i	−0.267003	+	0.154154i
$690$	24.5347	+	36.7074i	0.934021	+	1.39743i
$691$	7.62153	+	4.40029i	0.289937	+	0.167395i	0.637913	−	0.770108i	$-0.279798\pi$
$691$	7.62153	+	4.40029i	0.289937	+	0.167395i	−0.347977	+	0.937503i	$0.613131\pi$
$692$	−8.82582	−	10.5501i	−0.335507	−	0.401055i
$693$	0.882636	+	0.0369647i	0.0335286	+	0.00140417i
$694$	−18.2733	+	6.63553i	−0.693646	+	0.251881i
$695$	20.8497	−	36.1127i	0.790872	−	1.36983i
$696$	1.20939	+	4.97139i	0.0458420	+	0.188440i
$697$	22.2811	+	38.5920i	0.843957	+	1.46178i
$698$	−18.8299	−	15.8241i	−0.712723	−	0.598952i
$699$	42.1598	+	12.2478i	1.59463	+	0.463255i
$700$	18.5114	−	3.23560i	0.699663	−	0.122294i
$701$			40.0613i			1.51309i	0.653940	+	0.756546i	$0.273115\pi$
$701$			40.0613i			1.51309i	−0.653940	+	0.756546i	$0.726885\pi$
$702$	14.0392	−	25.7072i	0.529877	−	0.970254i
$703$			23.2975i			0.878682i
$704$	−2.35574	−	0.0105375i	−0.0887851	−	0.000397147i
$705$	21.2512	+	6.17368i	0.800367	+	0.232514i
$706$	−17.0949	+	20.3421i	−0.643375	+	0.765584i
$707$	6.43278	+	11.1419i	0.241930	+	0.419034i
$708$	28.5982	+	3.14944i	1.07479	+	0.118363i
$709$	−13.4387	+	23.2765i	−0.504701	+	0.874169i	0.495284	+	0.868731i	$0.335064\pi$
$709$	−13.4387	+	23.2765i	−0.504701	+	0.874169i	−0.999985	+	0.00543734i	$0.998269\pi$
$710$	5.00509	+	13.7833i	0.187838	+	0.517279i
$711$	−7.61985	−	14.5743i	−0.285767	−	0.546578i
$712$	8.20917	+	4.76408i	0.307652	+	0.178541i
$713$	26.4517	+	15.2719i	0.990622	+	0.571936i
$714$	7.34878	−	4.91183i	0.275021	−	0.183820i
$715$	3.85681	−	2.22673i	0.144237	−	0.0832751i
$716$	36.3416	+	13.2887i	1.35815	+	0.496621i
$717$	−42.3487	+	10.4026i	−1.58154	+	0.388491i
$718$	−3.51455	+	19.8455i	−0.131162	+	0.740627i
$719$	−40.6857			−1.51732			−0.758661	−	0.651486i	$-0.774146\pi$
$719$	−40.6857			−1.51732			−0.758661	+	0.651486i	$0.774146\pi$
$720$	33.5315	+	30.8003i	1.24965	+	1.14786i
$721$	8.91268			0.331925
$722$	−4.26865	+	24.1036i	−0.158863	+	0.897044i
$723$	11.5973	+	12.0932i	0.431310	+	0.449751i
$724$	23.8312	+	8.71409i	0.885678	+	0.323857i
$725$	8.49828	−	4.90649i	0.315618	−	0.182222i
$726$	−1.75218	−	26.6745i	−0.0650295	−	0.989984i
$727$	−3.36949	−	1.94538i	−0.124968	−	0.0721501i	0.436213	−	0.899843i	$-0.356319\pi$
$727$	−3.36949	−	1.94538i	−0.124968	−	0.0721501i	−0.561181	+	0.827693i	$0.689653\pi$
$728$	−9.75101	−	5.65886i	−0.361396	−	0.209731i
$729$	3.38138	−	26.7874i	0.125236	−	0.992127i
$730$	15.8108	+	43.5409i	0.585185	+	1.61152i
$731$	−1.77611	+	3.07631i	−0.0656918	+	0.113782i
$732$	−15.2864	−	34.7978i	−0.565001	−	1.28616i
$733$	−11.2371	−	19.4633i	−0.415053	−	0.718893i	0.580381	−	0.814345i	$-0.302904\pi$
$733$	−11.2371	−	19.4633i	−0.415053	−	0.718893i	−0.995434	+	0.0954521i	$0.969570\pi$
$734$	−1.97161	+	2.34612i	−0.0727734	+	0.0865968i
$735$	−4.74316	+	4.54867i	−0.174954	+	0.167780i
$736$	25.2186	+	9.28541i	0.929569	+	0.342265i
$737$		−	3.14915i		−	0.116000i
$738$	11.2870	−	51.1621i	0.415479	−	1.88330i
$739$			34.2290i			1.25913i	0.776947	+	0.629567i	$0.216768\pi$
$739$			34.2290i			1.25913i	−0.776947	+	0.629567i	$0.783232\pi$
$740$	−28.9014	+	5.05167i	−1.06244	+	0.185703i
$741$	9.92390	+	40.4000i	0.364563	+	1.48413i
$742$	2.19814	+	1.84726i	0.0806964	+	0.0678149i
$743$	−14.2792	−	24.7322i	−0.523851	−	0.907337i	−0.999615	−	0.0277637i	$-0.991161\pi$
$743$	−14.2792	−	24.7322i	−0.523851	−	0.907337i	0.475763	−	0.879573i	$-0.342172\pi$
$744$	30.2272	+	8.85465i	1.10818	+	0.324627i
$745$	−15.8246	+	27.4091i	−0.579770	+	1.00419i
$746$	−44.4843	+	16.1534i	−1.62869	+	0.591418i
$747$	−21.6458	+	11.3171i	−0.791980	+	0.414070i
$748$	1.36364	+	1.63006i	0.0498597	+	0.0596008i
$749$	1.97552	+	1.14057i	0.0721839	+	0.0416754i
$750$	18.0648	−	36.6451i	0.659634	−	1.33809i
$751$	−3.64406	+	2.10390i	−0.132974	+	0.0767723i	−0.565011	−	0.825083i	$-0.691128\pi$
$751$	−3.64406	+	2.10390i	−0.132974	+	0.0767723i	0.432038	+	0.901856i	$0.357795\pi$
$752$	12.6710	−	4.56913i	0.462064	−	0.166619i
$753$	4.47970	−	15.4202i	0.163249	−	0.561942i
$754$	−5.79700	−	1.02662i	−0.211114	−	0.0373874i
$755$	−20.0921			−0.731226
$756$	−10.2732	−	1.56884i	−0.373633	−	0.0570580i
$757$	−5.18894			−0.188595			−0.0942977	−	0.995544i	$-0.530061\pi$
$757$	−5.18894			−0.188595			−0.0942977	+	0.995544i	$0.530061\pi$
$758$	−9.51105	−	1.68437i	−0.345457	−	0.0611790i
$759$	0.675958	−	2.32681i	0.0245357	−	0.0844577i
$760$	−64.6654	−	0.144628i	−2.34566	−	0.00524620i
$761$	0.558714	−	0.322574i	0.0202534	−	0.0116933i	−0.489839	−	0.871813i	$-0.662944\pi$
$761$	0.558714	−	0.322574i	0.0202534	−	0.0116933i	0.510092	+	0.860120i	$0.329611\pi$
$762$	−7.57063	+	15.3573i	−0.274255	+	0.556335i
$763$	8.70733	+	5.02718i	0.315226	+	0.181996i
$764$	−12.7604	+	10.6748i	−0.461654	+	0.386202i
$765$	1.71871	−	41.0390i	0.0621400	−	1.48377i
$766$	−9.83434	+	3.57111i	−0.355329	+	0.129029i
$767$	−16.5528	+	28.6703i	−0.597688	+	1.03523i
$768$	27.5324	+	3.15678i	0.993491	+	0.113910i
$769$	−12.6215	−	21.8612i	−0.455145	−	0.788333i	0.543552	−	0.839376i	$-0.317079\pi$
$769$	−12.6215	−	21.8612i	−0.455145	−	0.788333i	−0.998697	+	0.0510420i	$0.983746\pi$
$770$	−1.20965	−	1.01655i	−0.0435927	−	0.0366340i
$771$	−5.80606	−	23.6364i	−0.209100	−	0.851243i
$772$	−3.71608	−	21.2603i	−0.133745	−	0.765174i
$773$		−	8.72610i		−	0.313856i	−0.987610	−	0.156928i	$-0.949841\pi$
$773$		−	8.72610i		−	0.313856i	0.987610	−	0.156928i	$-0.0501591\pi$
$774$	3.98180	−	1.25998i	0.143123	−	0.0452889i
$775$		−	60.4106i		−	2.17001i
$776$	18.9918	+	33.0654i	0.681768	+	1.18698i
$777$	4.83336	−	4.63517i	0.173396	−	0.166286i
$778$	15.7924	−	18.7922i	0.566187	−	0.673734i
$779$	37.2057	+	64.4421i	1.33303	+	2.30888i
$780$	−47.9658	+	21.0710i	−1.71745	+	0.754462i
$781$	0.402370	−	0.696926i	0.0143979	−	0.0249380i
$782$	−8.27492	−	22.7880i	−0.295910	−	0.814897i
$783$	−5.31963	+	1.07290i	−0.190108	+	0.0383422i
$784$	−0.706337	+	3.93714i	−0.0252263	+	0.140612i
$785$	−30.6869	−	17.7171i	−1.09526	−	0.632351i
$786$	−1.91002	−	29.0774i	−0.0681282	−	1.03716i
$787$	−16.8392	+	9.72212i	−0.600253	+	0.346556i	−0.769141	−	0.639079i	$-0.779316\pi$
$787$	−16.8392	+	9.72212i	−0.600253	+	0.346556i	0.168888	+	0.985635i	$0.445982\pi$
$788$	−9.88636	+	27.0370i	−0.352187	+	0.963155i
$789$	−9.50806	−	9.91460i	−0.338496	−	0.352969i
$790$	−5.12953	+	28.9647i	−0.182501	+	1.03052i
$791$	−7.01719			−0.249502
$792$	0.110135	−	2.49623i	0.00391348	−	0.0886997i
$793$	43.7334			1.55302
$794$	1.21088	−	6.83745i	0.0429727	−	0.242652i
$795$	12.9574	−	3.18287i	0.459552	−	0.112885i
$796$	−10.2975	+	28.1614i	−0.364984	+	0.998153i
$797$	−46.9719	+	27.1193i	−1.66383	+	0.960614i	−0.692972	+	0.720964i	$0.743699\pi$
$797$	−46.9719	+	27.1193i	−1.66383	+	0.960614i	−0.970859	+	0.239649i	$0.922967\pi$
$798$	12.2712	−	8.20191i	0.434397	−	0.290345i
$799$	−10.5235	−	6.07577i	−0.372296	−	0.214945i
$800$	−9.03453	−	52.3783i	−0.319419	−	1.85185i
$801$	−5.39398	+	8.50016i	−0.190587	+	0.300338i
$802$	11.7255	+	32.2905i	0.414042	+	1.14022i
$803$	1.27107	−	2.20155i	0.0448550	−	0.0776911i
$804$	−4.05527	+	36.8235i	−0.143018	+	1.29866i
$805$	9.01246	+	15.6100i	0.317647	+	0.550182i
$806$	−23.3171	+	27.7462i	−0.821309	+	0.977317i
$807$	10.5863	+	3.07542i	0.372656	+	0.108260i
$808$	31.5547	−	18.1241i	1.11009	−	0.637604i
$809$		−	33.5957i		−	1.18116i	−0.806979	−	0.590581i	$-0.798899\pi$
$809$		−	33.5957i		−	1.18116i	0.806979	−	0.590581i	$-0.201101\pi$
$810$	−34.0518	+	34.2437i	−1.19646	+	1.20320i
$811$		−	6.28139i		−	0.220570i	−0.993900	−	0.110285i	$-0.964824\pi$
$811$		−	6.28139i		−	0.220570i	0.993900	−	0.110285i	$-0.0351763\pi$
$812$	0.359641	+	2.05756i	0.0126209	+	0.0722062i
$813$	4.96061	+	1.44110i	0.173976	+	0.0505417i
$814$	1.23265	+	1.03588i	0.0432044	+	0.0363077i
$815$	29.7125	+	51.4635i	1.04078	+	1.80269i
$816$	−13.8462	−	20.8165i	−0.484715	−	0.728724i
$817$	−2.96580	+	5.13692i	−0.103760	+	0.179718i
$818$	50.8583	−	18.4680i	1.77822	−	0.645718i
$819$	6.40707	−	10.0967i	0.223881	−	0.352806i
$820$	−71.8752	+	60.1281i	−2.50999	+	2.09976i
$821$	16.5450	+	9.55229i	0.577426	+	0.333377i	0.760110	−	0.649795i	$-0.225145\pi$
$821$	16.5450	+	9.55229i	0.577426	+	0.333377i	−0.182684	+	0.983172i	$0.558478\pi$
$822$	0.377873	+	0.565352i	0.0131798	+	0.0197189i
$823$	43.0543	−	24.8574i	1.50078	−	0.866476i	0.500780	−	0.865574i	$-0.333046\pi$
$823$	43.0543	−	24.8574i	1.50078	−	0.866476i	1.00000		0.000901331i	$-0.000286903\pi$
$824$	0.0563808	−	25.2088i	0.00196412	−	0.878190i
$825$	−4.65395	+	1.14320i	−0.162030	+	0.0398011i
$826$	11.5658	+	2.04825i	0.402425	+	0.0712678i
$827$	4.74479			0.164992			0.0824962	−	0.996591i	$-0.473711\pi$
$827$	4.74479			0.164992			0.0824962	+	0.996591i	$0.473711\pi$
$828$	−10.9004	+	26.3373i	−0.378815	+	0.915283i
$829$	11.3890			0.395558			0.197779	−	0.980247i	$-0.436627\pi$
$829$	11.3890			0.395558			0.197779	+	0.980247i	$0.436627\pi$
$830$	43.0187	+	7.61843i	1.49320	+	0.264440i
$831$	25.8654	+	26.9713i	0.897260	+	0.935624i
$832$	−16.0673	+	27.5442i	−0.557034	+	0.954922i
$833$	3.12511	−	1.80429i	0.108279	−	0.0625148i
$834$	26.8626	−	1.76454i	0.930177	−	0.0611010i
$835$	−9.42707	−	5.44272i	−0.326237	−	0.188353i
$836$	2.27705	+	2.72192i	0.0787535	+	0.0941395i
$837$	−10.6543	+	31.6637i	−0.368266	+	1.09446i
$838$	−25.1887	+	9.14669i	−0.870130	+	0.315967i
$839$	−17.0108	+	29.4636i	−0.587279	+	1.01720i	0.407308	+	0.913291i	$0.366468\pi$
$839$	−17.0108	+	29.4636i	−0.587279	+	1.01720i	−0.994587	+	0.103906i	$0.966866\pi$
$840$	12.8356	+	13.4444i	0.442869	+	0.463877i
$841$	−13.9546	−	24.1701i	−0.481194	−	0.833453i
$842$	−22.9600	−	19.2949i	−0.791253	−	0.664946i
$843$	−10.1049	+	9.69056i	−0.348031	+	0.333761i
$844$	−5.65238	+	0.987980i	−0.194563	+	0.0340077i
$845$		−	10.9581i		−	0.376970i
$846$	4.31016	+	13.6210i	0.148186	+	0.468301i
$847$		−	10.9133i		−	0.374985i
$848$	5.23872	−	6.20559i	0.179898	−	0.213101i
$849$	0.343401	+	1.39798i	0.0117855	+	0.0479785i
$850$	−30.8494	+	36.7092i	−1.05812	+	1.25912i
$851$	−9.18385	−	15.9069i	−0.314818	−	0.545281i
$852$	−5.60243	+	7.63112i	−0.191936	+	0.261438i
$853$	8.54802	−	14.8056i	0.292679	−	0.506934i	−0.681764	−	0.731573i	$-0.738787\pi$
$853$	8.54802	−	14.8056i	0.292679	−	0.506934i	0.974442	+	0.224638i	$0.0721201\pi$
$854$	−5.29607	−	14.5846i	−0.181228	−	0.499076i
$855$	2.86995	−	68.5282i	0.0981502	−	2.34361i
$856$	3.23850	−	5.58038i	0.110690	−	0.190734i
$857$	−4.25999	−	2.45951i	−0.145518	−	0.0840151i	0.425473	−	0.904971i	$-0.360108\pi$
$857$	−4.25999	−	2.45951i	−0.145518	−	0.0840151i	−0.570991	+	0.820956i	$0.693441\pi$
$858$	2.57878	+	1.27125i	0.0880381	+	0.0433999i
$859$	25.8381	−	14.9176i	0.881585	−	0.508983i	0.0104044	−	0.999946i	$-0.496688\pi$
$859$	25.8381	−	14.9176i	0.881585	−	0.508983i	0.871181	+	0.490963i	$0.163355\pi$
$860$	−7.01561	−	2.56533i	−0.239230	−	0.0874769i
$861$	5.96703	−	20.5399i	0.203356	−	0.699998i
$862$	−1.53898	+	8.69008i	−0.0524177	+	0.295985i
$863$	7.21912			0.245742			0.122871	−	0.992423i	$-0.460790\pi$
$863$	7.21912			0.245742			0.122871	+	0.992423i	$0.460790\pi$
$864$	−4.50231	+	29.0470i	−0.153172	+	0.988200i
$865$	−26.0946			−0.887244
$866$	3.01639	−	17.0325i	0.102501	−	0.578788i
$867$	1.92228	−	6.61692i	0.0652839	−	0.224722i
$868$	12.0767	+	4.41597i	0.409911	+	0.149888i
$869$	1.39801	−	0.807143i	0.0474243	−	0.0273804i
$870$	8.70594	+	4.29174i	0.295159	+	0.145504i
$871$	−36.9164	−	21.3137i	−1.25086	−	0.722186i
$872$	14.2741	−	24.5962i	0.483380	−	0.832932i
$873$	−35.8415	+	18.7390i	−1.21305	+	0.634218i
$874$	−13.8177	−	38.0521i	−0.467391	−	1.28713i
$875$	8.33966	−	14.4447i	0.281932	−	0.488321i
$876$	−17.6978	+	24.1063i	−0.597954	+	0.814477i
$877$	−4.56875	−	7.91331i	−0.154276	−	0.267214i	0.778519	−	0.627621i	$-0.215971\pi$
$877$	−4.56875	−	7.91331i	−0.154276	−	0.267214i	−0.932795	+	0.360407i	$0.882638\pi$
$878$	18.3472	−	21.8323i	0.619190	−	0.736805i
$879$	−5.38885	−	21.9379i	−0.181761	−	0.739948i
$880$	−2.88289	+	3.41496i	−0.0971822	+	0.115118i
$881$		−	18.1037i		−	0.609930i	−0.952364	−	0.304965i	$-0.901355\pi$
$881$		−	18.1037i		−	0.609930i	0.952364	−	0.304965i	$-0.0986447\pi$
$882$	−4.14302	−	0.913999i	−0.139503	−	0.0307759i
$883$		−	10.5545i		−	0.355187i	−0.984104	−	0.177593i	$-0.943169\pi$
$883$		−	10.5545i		−	0.355187i	0.984104	−	0.177593i	$-0.0568311\pi$
$884$	28.3378	−	4.95317i	0.953104	−	0.166593i
$885$	39.3943	−	37.7790i	1.32423	−	1.26993i
$886$	30.7540	+	25.8447i	1.03320	+	0.868271i
$887$	−4.71464	−	8.16599i	−0.158302	−	0.274187i	0.775954	−	0.630789i	$-0.217269\pi$
$887$	−4.71464	−	8.16599i	−0.158302	−	0.274187i	−0.934256	+	0.356602i	$0.883935\pi$
$888$	−13.0796	−	13.7001i	−0.438924	−	0.459745i
$889$	−3.49500	+	6.05351i	−0.117218	+	0.203028i
$890$	16.9249	−	6.14586i	0.567323	−	0.206010i
$891$	2.64095	+	0.221594i	0.0884751	+	0.00742367i
$892$	−21.5548	−	25.7660i	−0.721709	−	0.862709i
$893$	−17.5725	−	10.1455i	−0.588042	−	0.339506i
$894$	−20.3884	+	1.33926i	−0.681891	+	0.0447917i
$895$	63.5735	−	36.7042i	2.12503	−	1.22689i
$896$	11.1314	+	2.02272i	0.371875	+	0.0675744i
$897$	−22.7014	−	23.6720i	−0.757977	−	0.790386i
$898$	−12.3741	−	2.19140i	−0.412929	−	0.0731280i
$899$	6.71471			0.223948
$900$	55.8916	−	7.37457i	1.86305	−	0.245819i
$901$	−7.32646			−0.244080
$902$	5.06386	+	0.896788i	0.168608	+	0.0298598i
$903$	1.65578	−	0.406727i	0.0551010	−	0.0135350i
$904$	−0.0443901	+	19.8476i	−0.00147639	+	0.660120i
$905$	41.6886	−	24.0689i	1.38578	−	0.800078i
$906$	−7.20795	−	10.7841i	−0.239468	−	0.358278i
$907$	5.60015	+	3.23325i	0.185950	+	0.107358i	0.590085	−	0.807341i	$-0.299094\pi$
$907$	5.60015	+	3.23325i	0.185950	+	0.107358i	−0.404135	+	0.914699i	$0.632428\pi$
$908$	−44.1457	+	36.9306i	−1.46503	+	1.22558i
$909$	17.8828	+	34.2039i	0.593135	+	1.13447i
$910$	−20.1037	+	7.30017i	−0.666431	+	0.241998i
$911$	17.1240	−	29.6597i	0.567345	−	0.982670i	−0.429482	−	0.903075i	$-0.641304\pi$
$911$	17.1240	−	29.6597i	0.567345	−	0.982670i	0.996827	−	0.0795950i	$-0.0253627\pi$
$912$	−23.1208	−	34.7601i	−0.765607	−	1.15102i
$913$	−1.19878	−	2.07634i	−0.0396737	−	0.0687168i
$914$	−11.7730	−	9.89371i	−0.389417	−	0.327255i
$915$	−69.2413	−	20.1152i	−2.28905	−	0.664989i
$916$	6.40965	+	36.6706i	0.211781	+	1.21163i
$917$		−	11.8964i		−	0.392853i
$918$	22.6436	−	13.8001i	0.747351	−	0.455471i
$919$		−	7.16854i		−	0.236468i	−0.992986	−	0.118234i	$-0.962277\pi$
$919$		−	7.16854i		−	0.236468i	0.992986	−	0.118234i	$-0.0377233\pi$
$920$	44.2088	−	25.3923i	1.45752	−	0.837158i
$921$	54.2359	+	15.7560i	1.78713	+	0.519179i
$922$	32.9097	−	39.1609i	1.08382	−	1.28969i
$923$	−5.44654	−	9.43369i	−0.179275	−	0.310514i
$924$	0.111663	−	1.01394i	0.00367344	−	0.0333563i
$925$	−18.1642	+	31.4612i	−0.597234	+	1.03444i
$926$	4.18562	+	11.5266i	0.137548	+	0.378789i
$927$	26.7146	+	1.11880i	0.877423	+	0.0367463i
$928$	5.82192	−	1.00420i	0.191114	−	0.0329645i
$929$	20.4211	+	11.7901i	0.669993	+	0.386821i	0.796074	−	0.605199i	$-0.206907\pi$
$929$	20.4211	+	11.7901i	0.669993	+	0.386821i	−0.126081	+	0.992020i	$0.540240\pi$
$930$	49.6788	−	33.2046i	1.62903	−	1.08882i
$931$	5.21841	−	3.01285i	0.171026	−	0.0987422i
$932$	17.4096	−	47.6115i	0.570270	−	1.55957i
$933$	−21.7983	+	5.35454i	−0.713643	+	0.175300i
$934$	3.32910	−	18.7983i	0.108932	−	0.615100i
$935$	4.03178			0.131853
$936$	−28.5171	−	18.1858i	−0.932109	−	0.594420i
$937$	28.9176			0.944698			0.472349	−	0.881411i	$-0.343406\pi$
$937$	28.9176			0.944698			0.472349	+	0.881411i	$0.343406\pi$
$938$	−2.63736	+	14.8923i	−0.0861129	+	0.486250i
$939$	8.92194	+	9.30341i	0.291157	+	0.303605i
$940$	8.77554	−	23.9992i	0.286227	−	0.782767i
$941$	−7.14862	+	4.12726i	−0.233038	+	0.134545i	−0.611973	−	0.790879i	$-0.709624\pi$
$941$	−7.14862	+	4.12726i	−0.233038	+	0.134545i	0.378935	+	0.925423i	$0.376291\pi$
$942$	−1.49943	−	22.8267i	−0.0488540	−	0.743733i
$943$	−50.8060	−	29.3328i	−1.65447	−	0.955208i
$944$	5.86648	−	32.7000i	0.190938	−	1.06429i
$945$	−14.7880	+	13.0387i	−0.481054	+	0.424148i
$946$	0.139921	+	0.385322i	0.00454921	+	0.0125279i
$947$	−13.0431	+	22.5914i	−0.423845	+	0.734121i	−0.996312	−	0.0858067i	$-0.972653\pi$
$947$	−13.0431	+	22.5914i	−0.423845	+	0.734121i	0.572467	+	0.819928i	$0.305987\pi$
$948$	−17.3866	+	7.63778i	−0.564690	+	0.248064i
$949$	−17.2054	−	29.8006i	−0.558510	−	0.967367i
$950$	−51.5132	+	61.2982i	−1.67131	+	1.98878i
$951$	−0.392970	+	0.376857i	−0.0127429	+	0.0122204i
$952$	−5.08351	−	8.85055i	−0.164757	−	0.286848i
$953$			8.16427i			0.264467i	0.991219	+	0.132233i	$0.0422148\pi$
$953$			8.16427i			0.264467i	−0.991219	+	0.132233i	$0.957785\pi$
$954$	6.35677	+	5.81285i	0.205808	+	0.188198i
$955$			31.5615i			1.02131i
$956$	8.66990	+	49.6018i	0.280404	+	1.60424i
$957$	−0.127068	−	0.517293i	−0.00410753	−	0.0167217i
$958$	41.4465	+	34.8304i	1.33908	+	1.12532i
$959$	0.138806	+	0.240419i	0.00448228	+	0.00776354i
$960$	38.1077	−	36.2193i	1.22992	−	1.16897i
$961$	5.16854	−	8.95217i	0.166727	−	0.288780i
$962$	20.4860	−	7.43900i	0.660495	−	0.239843i
$963$	5.77819	+	3.66669i	0.186200	+	0.118157i
$964$	14.8396	−	12.4142i	0.477950	−	0.399835i
$965$	−35.4589	−	20.4722i	−1.14146	−	0.659024i
$966$	−5.14526	+	10.4373i	−0.165546	+	0.335816i
$967$	−47.9368	+	27.6763i	−1.54154	+	0.890010i	−0.542800	+	0.839862i	$0.682636\pi$
$967$	−47.9368	+	27.6763i	−1.54154	+	0.890010i	−0.998742	+	0.0501481i	$0.984031\pi$
$968$	−30.8674	−	0.0690365i	−0.992115	−	0.00221892i
$969$	−10.5068	+	36.1667i	−0.337526	+	1.16184i
$970$	71.2310	+	12.6147i	2.28709	+	0.405034i
$971$	11.2138			0.359869			0.179935	−	0.983679i	$-0.442411\pi$
$971$	11.2138			0.359869			0.179935	+	0.983679i	$0.442411\pi$
$972$	−30.5957	−	5.99197i	−0.981357	−	0.192193i
$973$	10.9903			0.352332
$974$	−18.5366	−	3.28275i	−0.593951	−	0.105186i
$975$	−18.0970	+	62.2940i	−0.579567	+	1.99500i
$976$	−41.2850	+	14.8872i	−1.32150	+	0.476529i
$977$	−20.0276	+	11.5629i	−0.640740	+	0.369931i	−0.784899	−	0.619623i	$-0.787285\pi$
$977$	−20.0276	+	11.5629i	−0.640740	+	0.369931i	0.144160	+	0.989554i	$0.453952\pi$
$978$	−16.9630	+	34.4100i	−0.542418	+	1.10031i
$979$	−0.855770	−	0.494079i	−0.0273505	−	0.0157908i
$980$	4.86906	+	5.82033i	0.155537	+	0.185924i
$981$	25.4680	+	16.1613i	0.813132	+	0.515992i
$982$	3.90106	−	1.41658i	0.124488	−	0.0452048i
$983$	16.6695	−	28.8724i	0.531673	−	0.920885i	−0.467643	−	0.883917i	$-0.654897\pi$
$983$	16.6695	−	28.8724i	0.531673	−	0.920885i	0.999316	−	0.0369680i	$-0.0117700\pi$
$984$	−58.0577	−	17.0072i	−1.85081	−	0.542170i
$985$	27.3068	+	47.2967i	0.870067	+	1.50700i
$986$	−4.08028	−	3.42895i	−0.129943	−	0.109200i
$987$	1.39135	+	5.66415i	0.0442870	+	0.180292i
$988$	47.3193	−	8.27095i	1.50543	−	0.263134i
$989$		−	4.67646i		−	0.148703i
$990$	−3.49816	−	3.19883i	−0.111179	−	0.101666i
$991$		−	27.6317i		−	0.877749i	−0.898548	−	0.438875i	$-0.855377\pi$
$991$		−	27.6317i		−	0.877749i	0.898548	−	0.438875i	$-0.144623\pi$
$992$	12.5666	−	34.1301i	0.398991	−	1.08363i
$993$	26.3412	−	25.2611i	0.835911	−	0.801636i
$994$	−2.48647	+	2.95877i	−0.0788660	+	0.0938466i
$995$	28.4423	+	49.2635i	0.901682	+	1.56176i
$996$	11.3437	+	25.8227i	0.359439	+	0.818223i
$997$	10.1065	−	17.5050i	0.320077	−	0.554390i	−0.660426	−	0.750891i	$-0.729624\pi$
$997$	10.1065	−	17.5050i	0.320077	−	0.554390i	0.980504	+	0.196500i	$0.0629577\pi$
$998$	−18.0305	−	49.6536i	−0.570746	−	1.57176i
$999$	15.0692	−	13.2866i	0.476769	−	0.420370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.21	yes	72
3.2	odd	2		756.2.ba.a.575.16		72
4.3	odd	2	inner	252.2.ba.a.155.10	✓	72
9.4	even	3		756.2.ba.a.71.27		72
9.5	odd	6	inner	252.2.ba.a.239.10	yes	72
12.11	even	2		756.2.ba.a.575.27		72
36.23	even	6	inner	252.2.ba.a.239.21	yes	72
36.31	odd	6		756.2.ba.a.71.16		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.10	✓	72	4.3	odd	2	inner
252.2.ba.a.155.21	yes	72	1.1	even	1	trivial
252.2.ba.a.239.10	yes	72	9.5	odd	6	inner
252.2.ba.a.239.21	yes	72	36.23	even	6	inner
756.2.ba.a.71.16		72	36.31	odd	6
756.2.ba.a.71.27		72	9.4	even	3
756.2.ba.a.575.16		72	3.2	odd	2
756.2.ba.a.575.27		72	12.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.246614 - 1.39255i) q^{2} +(0.483200 - 1.66329i) q^{3} +(-1.87836 - 0.686842i) q^{4} +(-3.28588 + 1.89710i) q^{5} +(-2.19704 - 1.08307i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.41969 + 2.44632i) q^{8} +(-2.53304 - 1.60740i) q^{9} +O(q^{10})\)	\(q+(0.246614 - 1.39255i) q^{2} +(0.483200 - 1.66329i) q^{3} +(-1.87836 - 0.686842i) q^{4} +(-3.28588 + 1.89710i) q^{5} +(-2.19704 - 1.08307i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-1.41969 + 2.44632i) q^{8} +(-2.53304 - 1.60740i) q^{9} +(1.83146 + 5.04359i) q^{10} +(0.147235 - 0.255018i) q^{11} +(-2.05004 + 2.79237i) q^{12} +(-1.99299 - 3.45197i) q^{13} +(-0.909846 + 1.08267i) q^{14} +(1.56769 + 6.38203i) q^{15} +(3.05650 + 2.58028i) q^{16} -3.60857i q^{17} +(-2.86306 + 3.13096i) q^{18} -6.02570i q^{19} +(7.47508 - 1.30657i) q^{20} +(-1.25011 + 1.19885i) q^{21} +(-0.318814 - 0.267922i) q^{22} +(2.37532 + 4.11418i) q^{23} +(3.38294 + 3.54341i) q^{24} +(4.69800 - 8.13717i) q^{25} +(-5.29852 + 1.92403i) q^{26} +(-3.89752 + 3.43647i) q^{27} +(1.28329 + 1.53400i) q^{28} +(0.904457 + 0.522189i) q^{29} +(9.27388 - 0.609178i) q^{30} +(5.56802 - 3.21470i) q^{31} +(4.34693 - 3.61998i) q^{32} +(-0.353025 - 0.368119i) q^{33} +(-5.02510 - 0.889923i) q^{34} +3.79421 q^{35} +(3.65393 + 4.75907i) q^{36} -3.86636 q^{37} +(-8.39106 - 1.48602i) q^{38} +(-6.70462 + 1.64693i) q^{39} +(0.0240018 - 10.7316i) q^{40} +(-10.6945 + 6.17450i) q^{41} +(1.36116 + 2.03648i) q^{42} +(-0.852502 - 0.492192i) q^{43} +(-0.451718 + 0.377890i) q^{44} +(11.3726 + 0.476285i) q^{45} +(6.31496 - 2.29313i) q^{46} +(1.68371 - 2.91626i) q^{47} +(5.76863 - 3.83704i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-10.1728 - 8.54892i) q^{50} +(-6.00208 - 1.74366i) q^{51} +(1.37261 + 7.85292i) q^{52} -2.03029i q^{53} +(3.82425 + 6.27496i) q^{54} +1.11728i q^{55} +(2.45265 - 1.40873i) q^{56} +(-10.0225 - 2.91162i) q^{57} +(0.950223 - 1.13072i) q^{58} +(-4.15275 - 7.19278i) q^{59} +(1.43876 - 13.0645i) q^{60} +(-5.48589 + 9.50184i) q^{61} +(-3.10346 - 8.54650i) q^{62} +(1.38997 + 2.65857i) q^{63} +(-3.96897 - 6.94603i) q^{64} +(13.0975 + 7.56183i) q^{65} +(-0.599682 + 0.400819i) q^{66} +(9.26153 - 5.34715i) q^{67} +(-2.47852 + 6.77821i) q^{68} +(7.99081 - 1.96287i) q^{69} +(0.935704 - 5.28360i) q^{70} +2.73284 q^{71} +(7.52833 - 3.91461i) q^{72} +8.63292 q^{73} +(-0.953498 + 5.38408i) q^{74} +(-11.2644 - 11.7460i) q^{75} +(-4.13870 + 11.3185i) q^{76} +(-0.255018 + 0.147235i) q^{77} +(0.639970 + 9.74264i) q^{78} +(4.74756 + 2.74100i) q^{79} +(-14.9383 - 2.67999i) q^{80} +(3.83254 + 8.14319i) q^{81} +(5.96084 + 16.4153i) q^{82} +(4.07096 - 7.05111i) q^{83} +(3.17157 - 1.39325i) q^{84} +(6.84583 + 11.8573i) q^{85} +(-0.895639 + 1.06577i) q^{86} +(1.30558 - 1.25205i) q^{87} +(0.414829 + 0.722231i) q^{88} -3.35572i q^{89} +(3.46790 - 15.7195i) q^{90} +3.98599i q^{91} +(-1.63593 - 9.35939i) q^{92} +(-2.65649 - 10.8145i) q^{93} +(-3.64580 - 3.06383i) q^{94} +(11.4314 + 19.7997i) q^{95} +(-3.92062 - 8.97935i) q^{96} +(6.74076 - 11.6753i) q^{97} +(1.32929 - 0.482699i) q^{98} +(-0.782868 + 0.409306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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