LMFDB - Embedded newform 231.2.p.a.10.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(10,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.p (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.10
Character	$\chi$	$=$	231.10
Dual form			231.2.p.a.208.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.533044 - 0.307753i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.810576 + 1.40396i) q^{4} +(2.84562 - 1.64292i) q^{5} +0.615506 q^{6} +(-0.613452 + 2.57365i) q^{7} +2.22884i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.533044 - 0.307753i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.810576 + 1.40396i) q^{4} +(2.84562 - 1.64292i) q^{5} +0.615506 q^{6} +(-0.613452 + 2.57365i) q^{7} +2.22884i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.01123 - 1.75150i) q^{10} +(-2.83889 - 1.71485i) q^{11} +(-1.40396 + 0.810576i) q^{12} +0.142630 q^{13} +(0.465052 + 1.56066i) q^{14} +3.28584 q^{15} +(-0.935219 - 1.61985i) q^{16} +(3.63184 - 6.29053i) q^{17} +(0.533044 + 0.307753i) q^{18} +(0.434571 + 0.752699i) q^{19} +5.32684i q^{20} +(-1.81809 + 1.92212i) q^{21} +(-2.04100 - 0.0404149i) q^{22} +(1.78154 + 3.08572i) q^{23} +(-1.11442 + 1.93023i) q^{24} +(2.89836 - 5.02011i) q^{25} +(0.0760278 - 0.0438947i) q^{26} +1.00000i q^{27} +(-3.11605 - 2.94740i) q^{28} +3.70637i q^{29} +(1.75150 - 1.01123i) q^{30} +(-4.17493 - 2.41040i) q^{31} +(-4.85749 - 2.80448i) q^{32} +(-1.60112 - 2.90455i) q^{33} -4.47084i q^{34} +(2.48265 + 8.33148i) q^{35} -1.62115 q^{36} +(-4.69635 - 8.13432i) q^{37} +(0.463291 + 0.267481i) q^{38} +(0.123521 + 0.0713148i) q^{39} +(3.66181 + 6.34243i) q^{40} -3.19487 q^{41} +(-0.377583 + 1.58410i) q^{42} -9.66641i q^{43} +(4.70872 - 2.59566i) q^{44} +(2.84562 + 1.64292i) q^{45} +(1.89928 + 1.09655i) q^{46} +(-7.58896 + 4.38149i) q^{47} -1.87044i q^{48} +(-6.24735 - 3.15762i) q^{49} -3.56792i q^{50} +(6.29053 - 3.63184i) q^{51} +(-0.115612 + 0.200246i) q^{52} +(3.31269 - 5.73774i) q^{53} +(0.307753 + 0.533044i) q^{54} +(-10.8958 - 0.215752i) q^{55} +(-5.73626 - 1.36729i) q^{56} +0.869142i q^{57} +(1.14065 + 1.97566i) q^{58} +(-1.33978 - 0.773522i) q^{59} +(-2.66342 + 4.61318i) q^{60} +(7.62645 + 13.2094i) q^{61} -2.96723 q^{62} +(-2.53557 + 0.755561i) q^{63} +0.288529 q^{64} +(0.405869 - 0.234329i) q^{65} +(-1.74735 - 1.05550i) q^{66} +(-6.50785 + 11.2719i) q^{67} +(5.88777 + 10.1979i) q^{68} +3.56308i q^{69} +(3.88740 + 3.67700i) q^{70} +2.66532 q^{71} +(-1.93023 + 1.11442i) q^{72} +(-2.74419 + 4.75307i) q^{73} +(-5.00673 - 2.89064i) q^{74} +(5.02011 - 2.89836i) q^{75} -1.40901 q^{76} +(6.15495 - 6.25433i) q^{77} +0.0877894 q^{78} +(6.10848 - 3.52673i) q^{79} +(-5.32255 - 3.07298i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.70300 + 0.983230i) q^{82} +6.31032 q^{83} +(-1.22488 - 4.11055i) q^{84} -23.8673i q^{85} +(-2.97487 - 5.15263i) q^{86} +(-1.85319 + 3.20981i) q^{87} +(3.82213 - 6.32743i) q^{88} +(6.82310 - 3.93932i) q^{89} +2.02245 q^{90} +(-0.0874963 + 0.367079i) q^{91} -5.77630 q^{92} +(-2.41040 - 4.17493i) q^{93} +(-2.69683 + 4.67105i) q^{94} +(2.47325 + 1.42793i) q^{95} +(-2.80448 - 4.85749i) q^{96} +8.07193i q^{97} +(-4.30188 + 0.239492i) q^{98} +(0.0656613 - 3.31597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.533044	−	0.307753i	0.376919	−	0.217614i	−0.299558	−	0.954078i	$-0.596839\pi$
$2$	0.533044	−	0.307753i	0.376919	−	0.217614i	0.676477	+	0.736464i	$0.263506\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.810576	+	1.40396i	−0.405288	+	0.701979i
$5$	2.84562	−	1.64292i	1.27260	−	0.734735i	0.297123	−	0.954839i	$-0.403973\pi$
$5$	2.84562	−	1.64292i	1.27260	−	0.734735i	0.975476	+	0.220104i	$0.0706396\pi$
$6$	0.615506			0.251279
$7$	−0.613452	+	2.57365i	−0.231863	+	0.972748i
$7$	−0.613452	+	2.57365i	−0.231863	+	0.972748i
$8$			2.22884i			0.788015i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.01123	−	1.75150i	0.319778	−	0.553872i
$11$	−2.83889	−	1.71485i	−0.855957	−	0.517047i
$11$	−2.83889	−	1.71485i	−0.855957	−	0.517047i
$12$	−1.40396	+	0.810576i	−0.405288	+	0.233993i
$13$	0.142630			0.0395583			0.0197792	−	0.999804i	$-0.493704\pi$
$13$	0.142630			0.0395583			0.0197792	+	0.999804i	$0.493704\pi$
$14$	0.465052	+	1.56066i	0.124290	+	0.417104i
$15$	3.28584			0.848399
$16$	−0.935219	−	1.61985i	−0.233805	−	0.404962i
$17$	3.63184	−	6.29053i	0.880851	−	1.52568i	0.0304542	−	0.999536i	$-0.490305\pi$
$17$	3.63184	−	6.29053i	0.880851	−	1.52568i	0.850397	−	0.526142i	$-0.176362\pi$
$18$	0.533044	+	0.307753i	0.125640	+	0.0725381i
$19$	0.434571	+	0.752699i	0.0996974	+	0.172681i	0.911559	−	0.411168i	$-0.134879\pi$
$19$	0.434571	+	0.752699i	0.0996974	+	0.172681i	−0.811862	+	0.583849i	$0.801546\pi$
$20$			5.32684i			1.19112i
$21$	−1.81809	+	1.92212i	−0.396740	+	0.419441i
$22$	−2.04100	−	0.0404149i	−0.435143	−	0.00861650i
$23$	1.78154	+	3.08572i	0.371477	+	0.643417i	0.989793	−	0.142512i	$-0.0455181\pi$
$23$	1.78154	+	3.08572i	0.371477	+	0.643417i	−0.618316	+	0.785930i	$0.712185\pi$
$24$	−1.11442	+	1.93023i	−0.227480	+	0.394007i
$25$	2.89836	−	5.02011i	0.579672	−	1.00402i
$26$	0.0760278	−	0.0438947i	0.0149103	−	0.00860846i
$27$			1.00000i			0.192450i
$28$	−3.11605	−	2.94740i	−0.588878	−	0.557006i
$29$			3.70637i			0.688256i	0.938923	+	0.344128i	$0.111825\pi$
$29$			3.70637i			0.688256i	−0.938923	+	0.344128i	$0.888175\pi$
$30$	1.75150	−	1.01123i	0.319778	−	0.184624i
$31$	−4.17493	−	2.41040i	−0.749840	−	0.432921i	0.0757958	−	0.997123i	$-0.475850\pi$
$31$	−4.17493	−	2.41040i	−0.749840	−	0.432921i	−0.825636	+	0.564203i	$0.809184\pi$
$32$	−4.85749	−	2.80448i	−0.858692	−	0.495766i
$33$	−1.60112	−	2.90455i	−0.278720	−	0.505617i
$34$		−	4.47084i		−	0.766743i
$35$	2.48265	+	8.33148i	0.419644	+	1.40828i
$36$	−1.62115			−0.270192
$37$	−4.69635	−	8.13432i	−0.772076	−	1.33727i	−0.936423	−	0.350872i	$-0.885885\pi$
$37$	−4.69635	−	8.13432i	−0.772076	−	1.33727i	0.164348	−	0.986402i	$-0.447448\pi$
$38$	0.463291	+	0.267481i	0.0751557	+	0.0433912i
$39$	0.123521	+	0.0713148i	0.0197792	+	0.0114195i
$40$	3.66181	+	6.34243i	0.578982	+	1.00283i
$41$	−3.19487			−0.498954			−0.249477	−	0.968381i	$-0.580259\pi$
$41$	−3.19487			−0.498954			−0.249477	+	0.968381i	$0.580259\pi$
$42$	−0.377583	+	1.58410i	−0.0582624	+	0.244432i
$43$		−	9.66641i		−	1.47411i	−0.675831	−	0.737057i	$-0.736215\pi$
$43$		−	9.66641i		−	1.47411i	0.675831	−	0.737057i	$-0.263785\pi$
$44$	4.70872	−	2.59566i	0.709866	−	0.391311i
$45$	2.84562	+	1.64292i	0.424200	+	0.244912i
$46$	1.89928	+	1.09655i	0.280034	+	0.161678i
$47$	−7.58896	+	4.38149i	−1.10696	+	0.639106i	−0.938041	−	0.346524i	$-0.887362\pi$
$47$	−7.58896	+	4.38149i	−1.10696	+	0.639106i	−0.168922	+	0.985629i	$0.554029\pi$
$48$		−	1.87044i		−	0.269974i
$49$	−6.24735	−	3.15762i	−0.892479	−	0.451089i
$50$		−	3.56792i		−	0.504580i
$51$	6.29053	−	3.63184i	0.880851	−	0.508559i
$52$	−0.115612	+	0.200246i	−0.0160325	+	0.0277691i
$53$	3.31269	−	5.73774i	0.455032	−	0.788139i	−0.543658	−	0.839307i	$-0.682961\pi$
$53$	3.31269	−	5.73774i	0.455032	−	0.788139i	0.998690	+	0.0511679i	$0.0162944\pi$
$54$	0.307753	+	0.533044i	0.0418799	+	0.0725381i
$55$	−10.8958	−	0.215752i	−1.46918	−	0.0290920i
$56$	−5.73626	−	1.36729i	−0.766540	−	0.182711i
$57$			0.869142i			0.115121i
$58$	1.14065	+	1.97566i	0.149774	+	0.259417i
$59$	−1.33978	−	0.773522i	−0.174425	−	0.100704i	0.410246	−	0.911975i	$-0.365443\pi$
$59$	−1.33978	−	0.773522i	−0.174425	−	0.100704i	−0.584670	+	0.811271i	$0.698776\pi$
$60$	−2.66342	+	4.61318i	−0.343846	+	0.595559i
$61$	7.62645	+	13.2094i	0.976467	+	1.69129i	0.675008	+	0.737810i	$0.264140\pi$
$61$	7.62645	+	13.2094i	0.976467	+	1.69129i	0.301459	+	0.953479i	$0.402526\pi$
$62$	−2.96723			−0.376839
$63$	−2.53557	+	0.755561i	−0.319452	+	0.0951917i
$64$	0.288529			0.0360662
$65$	0.405869	−	0.234329i	0.0503419	−	0.0290649i
$66$	−1.74735	−	1.05550i	−0.215084	−	0.129923i
$67$	−6.50785	+	11.2719i	−0.795061	+	1.37709i	0.127740	+	0.991808i	$0.459228\pi$
$67$	−6.50785	+	11.2719i	−0.795061	+	1.37709i	−0.922801	+	0.385278i	$0.874106\pi$
$68$	5.88777	+	10.1979i	0.713996	+	1.23668i
$69$			3.56308i			0.428945i
$70$	3.88740	+	3.67700i	0.464633	+	0.439486i
$71$	2.66532			0.316315			0.158158	−	0.987414i	$-0.449445\pi$
$71$	2.66532			0.316315			0.158158	+	0.987414i	$0.449445\pi$
$72$	−1.93023	+	1.11442i	−0.227480	+	0.131336i
$73$	−2.74419	+	4.75307i	−0.321183	+	0.556305i	−0.980732	−	0.195356i	$-0.937414\pi$
$73$	−2.74419	+	4.75307i	−0.321183	+	0.556305i	0.659549	+	0.751661i	$0.270747\pi$
$74$	−5.00673	−	2.89064i	−0.582020	−	0.336030i
$75$	5.02011	−	2.89836i	0.579672	−	0.334674i
$76$	−1.40901			−0.161625
$77$	6.15495	−	6.25433i	0.701422	−	0.712747i
$78$	0.0877894			0.00994019
$79$	6.10848	−	3.52673i	0.687258	−	0.396789i	−0.115326	−	0.993328i	$-0.536791\pi$
$79$	6.10848	−	3.52673i	0.687258	−	0.396789i	0.802584	+	0.596539i	$0.203458\pi$
$80$	−5.32255	−	3.07298i	−0.595079	−	0.343569i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.70300	+	0.983230i	−0.188065	+	0.108580i
$83$	6.31032			0.692648			0.346324	−	0.938115i	$-0.387430\pi$
$83$	6.31032			0.692648			0.346324	+	0.938115i	$0.387430\pi$
$84$	−1.22488	−	4.11055i	−0.133645	−	0.448498i
$85$		−	23.8673i		−	2.58877i
$86$	−2.97487	−	5.15263i	−0.320788	−	0.555622i
$87$	−1.85319	+	3.20981i	−0.198682	+	0.344128i
$88$	3.82213	−	6.32743i	0.407441	−	0.674507i
$89$	6.82310	−	3.93932i	0.723247	−	0.417567i	−0.0926996	−	0.995694i	$-0.529550\pi$
$89$	6.82310	−	3.93932i	0.723247	−	0.417567i	0.815947	+	0.578127i	$0.196216\pi$
$90$	2.02245			0.213185
$91$	−0.0874963	+	0.367079i	−0.00917211	+	0.0384803i
$92$	−5.77630			−0.602221
$93$	−2.41040	−	4.17493i	−0.249947	−	0.432921i
$94$	−2.69683	+	4.67105i	−0.278157	+	0.481782i
$95$	2.47325	+	1.42793i	0.253750	+	0.146502i
$96$	−2.80448	−	4.85749i	−0.286231	−	0.495766i
$97$			8.07193i			0.819580i	0.912180	+	0.409790i	$0.134398\pi$
$97$			8.07193i			0.819580i	−0.912180	+	0.409790i	$0.865602\pi$
$98$	−4.30188	+	0.239492i	−0.434556	+	0.0241924i
$99$	0.0656613	−	3.31597i	0.00659921	−	0.333268i
$100$	4.69869	+	8.13836i	0.469869	+	0.813836i
$101$	−3.44804	+	5.97217i	−0.343092	+	0.594253i	−0.985005	−	0.172524i	$-0.944808\pi$
$101$	−3.44804	+	5.97217i	−0.343092	+	0.594253i	0.641913	+	0.766777i	$0.278141\pi$
$102$	2.23542	−	3.87186i	0.221340	−	0.383372i
$103$	2.99657	−	1.73007i	0.295261	−	0.170469i	−0.345051	−	0.938584i	$-0.612138\pi$
$103$	2.99657	−	1.73007i	0.295261	−	0.170469i	0.640312	+	0.768115i	$0.278805\pi$
$104$			0.317899i			0.0311725i
$105$	−2.01570	+	8.45660i	−0.196712	+	0.825279i
$106$		−	4.07796i		−	0.396086i
$107$	1.83718	−	1.06069i	0.177606	−	0.102541i	−0.408561	−	0.912731i	$-0.633969\pi$
$107$	1.83718	−	1.06069i	0.177606	−	0.102541i	0.586168	+	0.810190i	$0.300636\pi$
$108$	−1.40396	−	0.810576i	−0.135096	−	0.0779977i
$109$	−2.79255	−	1.61228i	−0.267478	−	0.154428i	0.360263	−	0.932851i	$-0.382687\pi$
$109$	−2.79255	−	1.61228i	−0.267478	−	0.154428i	−0.627741	+	0.778422i	$0.716020\pi$
$110$	−5.87432	+	3.23820i	−0.560094	+	0.308750i
$111$		−	9.39271i		−	0.891516i
$112$	4.74263	−	1.41323i	0.448136	−	0.133538i
$113$	11.8894			1.11846			0.559228	−	0.829014i	$-0.311098\pi$
$113$	11.8894			1.11846			0.559228	+	0.829014i	$0.311098\pi$
$114$	0.267481	+	0.463291i	0.0250519	+	0.0433912i
$115$	10.1392	+	5.85386i	0.945483	+	0.545875i
$116$	−5.20359	−	3.00430i	−0.483142	−	0.278942i
$117$	0.0713148	+	0.123521i	0.00659305	+	0.0114195i
$118$	−0.952216			−0.0876586
$119$	13.9617	+	13.2060i	1.27986	+	1.21059i
$120$			7.32361i			0.668551i
$121$	5.11857	+	9.73654i	0.465324	+	0.885140i
$122$	8.13047	+	4.69413i	0.736098	+	0.424986i
$123$	−2.76684	−	1.59743i	−0.249477	−	0.144036i
$124$	6.76820	−	3.90762i	0.607803	−	0.350915i
$125$		−	2.61791i		−	0.234153i
$126$	−1.11905	+	1.18308i	−0.0996925	+	0.105397i
$127$			15.6821i			1.39156i	0.718254	+	0.695781i	$0.244942\pi$
$127$			15.6821i			1.39156i	−0.718254	+	0.695781i	$0.755058\pi$
$128$	9.86879	−	5.69775i	0.872286	−	0.503614i
$129$	4.83321	−	8.37136i	0.425540	−	0.737057i
$130$	0.144231	−	0.249815i	0.0126499	−	0.0219102i
$131$	−5.01428	−	8.68500i	−0.438100	−	0.758812i	0.559443	−	0.828869i	$-0.311015\pi$
$131$	−5.01428	−	8.68500i	−0.438100	−	0.758812i	−0.997543	+	0.0700573i	$0.977682\pi$
$132$	5.37570	+	0.106447i	0.467895	+	0.00926502i
$133$	−2.20377	+	0.656689i	−0.191091	+	0.0569422i
$134$			8.01125i			0.692067i
$135$	1.64292	+	2.84562i	0.141400	+	0.244912i
$136$	14.0206	+	8.09480i	1.20226	+	0.694123i
$137$	−7.33923	+	12.7119i	−0.627033	+	1.08605i	0.361111	+	0.932523i	$0.382398\pi$
$137$	−7.33923	+	12.7119i	−0.627033	+	1.08605i	−0.988144	+	0.153530i	$0.950936\pi$
$138$	1.09655	+	1.89928i	0.0933446	+	0.161678i
$139$	4.45534			0.377897			0.188948	−	0.981987i	$-0.439492\pi$
$139$	4.45534			0.377897			0.188948	+	0.981987i	$0.439492\pi$
$140$	−13.7094	−	3.26776i	−1.15866	−	0.276176i
$141$	−8.76297			−0.737976
$142$	1.42073	−	0.820261i	0.119225	−	0.0688347i
$143$	−0.404909	−	0.244589i	−0.0338602	−	0.0204535i
$144$	0.935219	−	1.61985i	0.0779349	−	0.134987i
$145$	6.08927	+	10.5469i	0.505686	+	0.875874i
$146$			3.37813i			0.279576i
$147$	−3.83156	−	5.85826i	−0.316022	−	0.483181i
$148$	15.2270			1.25165
$149$	4.34391	−	2.50796i	0.355867	−	0.205460i	−0.311399	−	0.950279i	$-0.600798\pi$
$149$	4.34391	−	2.50796i	0.355867	−	0.205460i	0.667266	+	0.744819i	$0.267464\pi$
$150$	1.78396	−	3.08991i	0.145660	−	0.252290i
$151$	−12.7586	−	7.36619i	−1.03828	−	0.599452i	−0.118935	−	0.992902i	$-0.537948\pi$
$151$	−12.7586	−	7.36619i	−1.03828	−	0.599452i	−0.919346	+	0.393450i	$0.871281\pi$
$152$	−1.67765	+	0.968590i	−0.136075	+	0.0785630i
$153$	7.26368			0.587234
$154$	1.35607	−	5.22804i	0.109275	−	0.421287i
$155$	−15.8404			−1.27233
$156$	−0.200246	+	0.115612i	−0.0160325	+	0.00925637i
$157$	−8.97784	−	5.18336i	−0.716510	−	0.413677i	0.0969569	−	0.995289i	$-0.469089\pi$
$157$	−8.97784	−	5.18336i	−0.716510	−	0.413677i	−0.813467	+	0.581611i	$0.802422\pi$
$158$	2.17073	−	3.75981i	0.172694	−	0.299115i
$159$	5.73774	−	3.31269i	0.455032	−	0.262713i
$160$	−18.4301			−1.45703
$161$	−9.03446	+	2.69213i	−0.712015	+	0.212169i
$162$			0.615506i			0.0483588i
$163$	3.11119	+	5.38874i	0.243687	+	0.422078i	0.961762	−	0.273888i	$-0.0883097\pi$
$163$	3.11119	+	5.38874i	0.243687	+	0.422078i	−0.718075	+	0.695966i	$0.754976\pi$
$164$	2.58968	−	4.48546i	0.202220	−	0.350256i
$165$	−9.32812	−	5.63472i	−0.726193	−	0.438663i
$166$	3.36368	−	1.94202i	0.261072	−	0.150730i
$167$	21.3050			1.64863			0.824316	−	0.566129i	$-0.191560\pi$
$167$	21.3050			1.64863			0.824316	+	0.566129i	$0.191560\pi$
$168$	−4.28410	−	4.05224i	−0.330526	−	0.312637i
$169$	−12.9797			−0.998435
$170$	−7.34523	−	12.7223i	−0.563353	−	0.975757i
$171$	−0.434571	+	0.752699i	−0.0332325	+	0.0575603i
$172$	13.5712	+	7.83536i	1.03480	+	0.597441i
$173$	−0.748523	−	1.29648i	−0.0569091	−	0.0985695i	0.836167	−	0.548474i	$-0.184791\pi$
$173$	−0.748523	−	1.29648i	−0.0569091	−	0.0985695i	−0.893076	+	0.449905i	$0.851458\pi$
$174$			2.28130i			0.172945i
$175$	11.1420	+	10.5390i	0.842256	+	0.796671i
$176$	−0.122815	+	6.20232i	−0.00925755	+	0.467518i
$177$	−0.773522	−	1.33978i	−0.0581415	−	0.100704i
$178$	2.42468	−	4.19966i	0.181737	−	0.314778i
$179$	7.66328	−	13.2732i	0.572780	−	0.992084i	−0.423499	−	0.905897i	$-0.639198\pi$
$179$	7.66328	−	13.2732i	0.572780	−	0.992084i	0.996279	−	0.0861877i	$-0.0274685\pi$
$180$	−4.61318	+	2.66342i	−0.343846	+	0.198520i
$181$		−	14.5930i		−	1.08469i	−0.840156	−	0.542345i	$-0.817537\pi$
$181$		−	14.5930i		−	1.08469i	0.840156	−	0.542345i	$-0.182463\pi$
$182$	0.0663302	+	0.222596i	0.00491672	+	0.0164999i
$183$			15.2529i			1.12753i
$184$	−6.87759	+	3.97078i	−0.507022	+	0.292730i
$185$	−26.7281	−	15.4315i	−1.96509	−	1.13454i
$186$	−2.56970	−	1.48362i	−0.188419	−	0.108784i
$187$	−21.0977	+	11.6300i	−1.54282	+	0.850473i
$188$		−	14.2061i		−	1.03609i
$189$	−2.57365	−	0.613452i	−0.187206	−	0.0446220i
$190$	1.75780			0.127524
$191$	4.48581	+	7.76965i	0.324582	+	0.562192i	0.981428	−	0.191833i	$-0.0614432\pi$
$191$	4.48581	+	7.76965i	0.324582	+	0.562192i	−0.656846	+	0.754025i	$0.728110\pi$
$192$	0.249874	+	0.144265i	0.0180331	+	0.0104114i
$193$	−1.82904	−	1.05600i	−0.131657	−	0.0760123i	0.432725	−	0.901526i	$-0.357552\pi$
$193$	−1.82904	−	1.05600i	−0.131657	−	0.0760123i	−0.564382	+	0.825514i	$0.690885\pi$
$194$	2.48416	+	4.30269i	0.178352	+	0.308915i
$195$	0.468657			0.0335613
$196$	9.49712	−	6.21154i	0.678366	−	0.443681i
$197$		−	9.47897i		−	0.675348i	−0.941263	−	0.337674i	$-0.890360\pi$
$197$		−	9.47897i		−	0.675348i	0.941263	−	0.337674i	$-0.109640\pi$
$198$	−0.985501	−	1.78777i	−0.0700365	−	0.127051i
$199$	1.15409	+	0.666314i	0.0818112	+	0.0472337i	0.540348	−	0.841442i	$-0.318293\pi$
$199$	1.15409	+	0.666314i	0.0818112	+	0.0472337i	−0.458536	+	0.888676i	$0.651626\pi$
$200$	11.1890	+	6.45999i	0.791184	+	0.456790i
$201$	−11.2719	+	6.50785i	−0.795061	+	0.459029i
$202$			4.24458i			0.298647i
$203$	−9.53891	−	2.27368i	−0.669500	−	0.159581i
$204$			11.7755i			0.824452i
$205$	−9.09137	+	5.24890i	−0.634969	+	0.366599i
$206$	1.06487	−	1.84441i	0.0741930	−	0.128506i
$207$	−1.78154	+	3.08572i	−0.123826	+	0.214472i
$208$	−0.133390	−	0.231038i	−0.00924892	−	0.0160196i
$209$	0.0570690	−	2.88205i	0.00394754	−	0.199356i
$210$	1.52809	+	5.12808i	0.105448	+	0.353871i
$211$		−	5.34281i		−	0.367814i	−0.982944	−	0.183907i	$-0.941125\pi$
$211$		−	5.34281i		−	0.367814i	0.982944	−	0.183907i	$-0.0588745\pi$
$212$	5.37037	+	9.30175i	0.368838	+	0.638847i
$213$	2.30823	+	1.33266i	0.158158	+	0.0913123i
$214$	0.652864	−	1.13079i	0.0446289	−	0.0772995i
$215$	−15.8811	−	27.5069i	−1.08308	−	1.87596i
$216$	−2.22884			−0.151654
$217$	8.76465	−	9.26616i	0.594983	−	0.629028i
$218$	−1.98474			−0.134423
$219$	−4.75307	+	2.74419i	−0.321183	+	0.185435i
$220$	9.13474	−	15.1223i	0.615864	−	1.01955i
$221$	0.518008	−	0.897216i	0.0348450	−	0.0603533i
$222$	−2.89064	−	5.00673i	−0.194007	−	0.336030i
$223$			24.5309i			1.64271i	0.570415	+	0.821356i	$0.306782\pi$
$223$			24.5309i			1.64271i	−0.570415	+	0.821356i	$0.693218\pi$
$224$	10.1976	−	10.7811i	0.681354	−	0.720341i
$225$	5.79672			0.386448
$226$	6.33755	−	3.65899i	0.421568	−	0.243392i
$227$	−6.57841	+	11.3941i	−0.436625	+	0.756256i	−0.997427	−	0.0716939i	$-0.977160\pi$
$227$	−6.57841	+	11.3941i	−0.436625	+	0.756256i	0.560802	+	0.827950i	$0.310493\pi$
$228$	−1.22024	−	0.704506i	−0.0808123	−	0.0466570i
$229$	12.1770	−	7.03037i	0.804676	−	0.464580i	−0.0404273	−	0.999182i	$-0.512872\pi$
$229$	12.1770	−	7.03037i	0.804676	−	0.464580i	0.845104	+	0.534602i	$0.179539\pi$
$230$	7.20617			0.475161
$231$	8.45751	−	2.33893i	0.556463	−	0.153890i
$232$	−8.26092			−0.542356
$233$	−22.3875	+	12.9254i	−1.46666	+	0.846774i	−0.999304	−	0.0372980i	$-0.988125\pi$
$233$	−22.3875	+	12.9254i	−1.46666	+	0.846774i	−0.467351	+	0.884072i	$0.654792\pi$
$234$	0.0760278	+	0.0438947i	0.00497010	+	0.00286949i
$235$	−14.3969	+	24.9361i	−0.939147	+	1.62665i
$236$	2.17199	−	1.25400i	0.141384	−	0.0816283i
$237$	7.05347			0.458172
$238$	11.5064	+	2.74265i	0.745848	+	0.177779i
$239$			7.49156i			0.484589i	0.970203	+	0.242294i	$0.0779000\pi$
$239$			7.49156i			0.484589i	−0.970203	+	0.242294i	$0.922100\pi$
$240$	−3.07298	−	5.32255i	−0.198360	−	0.343569i
$241$	−9.07858	+	15.7246i	−0.584803	+	1.01291i	0.410098	+	0.912042i	$0.365495\pi$
$241$	−9.07858	+	15.7246i	−0.584803	+	1.01291i	−0.994900	+	0.100866i	$0.967839\pi$
$242$	5.72487	+	3.61475i	0.368009	+	0.232365i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−24.7273			−1.58300
$245$	−22.9653	+	1.27851i	−1.46720	+	0.0816811i
$246$	−1.96646			−0.125377
$247$	0.0619827	+	0.107357i	0.00394386	+	0.00683097i
$248$	5.37240	−	9.30527i	0.341148	−	0.590885i
$249$	5.46490	+	3.15516i	0.346324	+	0.199950i
$250$	−0.805669	−	1.39546i	−0.0509550	−	0.0882566i
$251$		−	3.07493i		−	0.194088i	−0.995280	−	0.0970441i	$-0.969061\pi$
$251$		−	3.07493i		−	0.194088i	0.995280	−	0.0970441i	$-0.0309388\pi$
$252$	0.994498	−	4.17228i	0.0626475	−	0.262829i
$253$	0.233957	−	11.8151i	0.0147087	−	0.742809i
$254$	4.82622	+	8.35926i	0.302824	+	0.524507i
$255$	11.9336	−	20.6697i	0.747313	−	1.29438i
$256$	3.21847	−	5.57455i	0.201154	−	0.348410i
$257$	−3.02050	+	1.74389i	−0.188414	+	0.108781i	−0.591240	−	0.806496i	$-0.701361\pi$
$257$	−3.02050	+	1.74389i	−0.188414	+	0.108781i	0.402826	+	0.915277i	$0.368028\pi$
$258$		−	5.94974i		−	0.370415i
$259$	23.8159	−	7.09676i	1.47985	−	0.440971i
$260$			0.759765i			0.0471186i
$261$	−3.20981	+	1.85319i	−0.198682	+	0.114709i
$262$	−5.34567	−	3.08632i	−0.330257	−	0.190674i
$263$	−5.59691	−	3.23138i	−0.345120	−	0.199255i	0.317414	−	0.948287i	$-0.397186\pi$
$263$	−5.59691	−	3.23138i	−0.345120	−	0.199255i	−0.662534	+	0.749032i	$0.730519\pi$
$264$	6.47378	−	3.56865i	0.398434	−	0.219635i
$265$		−	21.7699i		−	1.33731i
$266$	−0.972610	+	1.02826i	−0.0596345	+	0.0630468i
$267$	7.87864			0.482165
$268$	−10.5502	−	18.2735i	−0.644457	−	1.11623i
$269$	14.3284	+	8.27251i	0.873619	+	0.504384i	0.868549	−	0.495603i	$-0.165053\pi$
$269$	14.3284	+	8.27251i	0.873619	+	0.504384i	0.00506971	+	0.999987i	$0.498386\pi$
$270$	1.75150	+	1.01123i	0.106593	+	0.0615413i
$271$	−2.01849	−	3.49613i	−0.122615	−	0.212375i	0.798183	−	0.602415i	$-0.205795\pi$
$271$	−2.01849	−	3.49613i	−0.122615	−	0.212375i	−0.920798	+	0.390040i	$0.872461\pi$
$272$	−13.5863			−0.823788
$273$	−0.259313	+	0.274151i	−0.0156944	+	0.0165924i
$274$			9.03469i			0.545806i
$275$	−16.8369	+	9.28127i	−1.01530	+	0.559682i
$276$	−5.00242	−	2.88815i	−0.301110	−	0.173846i
$277$	2.12061	+	1.22434i	0.127415	+	0.0735632i	0.562353	−	0.826897i	$-0.309896\pi$
$277$	2.12061	+	1.22434i	0.127415	+	0.0735632i	−0.434938	+	0.900461i	$0.643230\pi$
$278$	2.37489	−	1.37114i	0.142437	−	0.0822358i
$279$		−	4.82080i		−	0.288614i
$280$	−18.5695	+	5.53343i	−1.10974	+	0.330686i
$281$		−	14.1901i		−	0.846509i	−0.906011	−	0.423254i	$-0.860888\pi$
$281$		−	14.1901i		−	0.846509i	0.906011	−	0.423254i	$-0.139112\pi$
$282$	−4.67105	+	2.69683i	−0.278157	+	0.160594i
$283$	−13.3403	+	23.1060i	−0.792997	+	1.37351i	0.131106	+	0.991368i	$0.458147\pi$
$283$	−13.3403	+	23.1060i	−0.792997	+	1.37351i	−0.924103	+	0.382143i	$0.875186\pi$
$284$	−2.16044	+	3.74200i	−0.128199	+	0.222047i
$285$	1.42793	+	2.47325i	0.0845832	+	0.146502i
$286$	−0.291107	−	0.00576437i	−0.0172135	−	0.000340854i
$287$	1.95990	−	8.22247i	0.115689	−	0.485357i
$288$		−	5.60895i		−	0.330511i
$289$	−17.8805	−	30.9700i	−1.05180	−	1.82176i
$290$	6.49170	+	3.74798i	0.381206	+	0.220089i
$291$	−4.03596	+	6.99049i	−0.236592	+	0.409790i
$292$	−4.44875	−	7.70546i	−0.260343	−	0.450928i
$293$	18.4082			1.07542			0.537708	−	0.843131i	$-0.319290\pi$
$293$	18.4082			1.07542			0.537708	+	0.843131i	$0.319290\pi$
$294$	−3.84529	−	1.94354i	−0.224262	−	0.113349i
$295$	−5.08334			−0.295963
$296$	18.1301	−	10.4674i	1.05379	−	0.608407i
$297$	1.71485	−	2.83889i	0.0995058	−	0.164729i
$298$	1.54366	−	2.67370i	0.0894220	−	0.154883i
$299$	0.254101	+	0.440115i	0.0146950	+	0.0254525i
$300$			9.39737i			0.542557i
$301$	24.8780	+	5.92988i	1.43394	+	0.341792i
$302$	−9.06787			−0.521798
$303$	−5.97217	+	3.44804i	−0.343092	+	0.198084i
$304$	0.812838	−	1.40788i	0.0466194	−	0.0807472i
$305$	43.4039	+	25.0593i	2.48530	+	1.43489i
$306$	3.87186	−	2.23542i	0.221340	−	0.127791i
$307$	−24.2462			−1.38380			−0.691902	−	0.721991i	$-0.743227\pi$
$307$	−24.2462			−1.38380			−0.691902	+	0.721991i	$0.743227\pi$
$308$	3.79176	+	13.7109i	0.216056	+	0.781251i
$309$	3.46014			0.196841
$310$	−8.44361	+	4.87492i	−0.479565	+	0.276877i
$311$	10.8566	+	6.26809i	0.615624	+	0.355431i	0.775163	−	0.631761i	$-0.217668\pi$
$311$	10.8566	+	6.26809i	0.615624	+	0.355431i	−0.159539	+	0.987192i	$0.551001\pi$
$312$	−0.158949	+	0.275308i	−0.00899874	+	0.0155863i
$313$	−8.28058	+	4.78080i	−0.468046	+	0.270227i	−0.715422	−	0.698693i	$-0.753765\pi$
$313$	−8.28058	+	4.78080i	−0.468046	+	0.270227i	0.247375	+	0.968920i	$0.420432\pi$
$314$	−6.38078			−0.360088
$315$	−5.97395	+	6.31578i	−0.336594	+	0.355854i
$316$			11.4347i			0.643255i
$317$	6.91454	+	11.9763i	0.388359	+	0.672658i	0.992229	−	0.124425i	$-0.0397087\pi$
$317$	6.91454	+	11.9763i	0.388359	+	0.672658i	−0.603870	+	0.797083i	$0.706375\pi$
$318$	2.03898	−	3.53162i	0.114340	−	0.198043i
$319$	6.35588	−	10.5220i	0.355861	−	0.589118i
$320$	0.821044	−	0.474030i	0.0458978	−	0.0264991i
$321$	2.12139			0.118404
$322$	−3.98726	+	4.21541i	−0.222201	+	0.234915i
$323$	6.31317			0.351274
$324$	−0.810576	−	1.40396i	−0.0450320	−	0.0779977i
$325$	0.413392	−	0.716016i	0.0229309	−	0.0397174i
$326$	3.31680	+	1.91496i	0.183701	+	0.106060i
$327$	−1.61228	−	2.79255i	−0.0891592	−	0.154428i
$328$		−	7.12085i		−	0.393183i
$329$	−6.62096	−	22.2192i	−0.365025	−	1.22498i
$330$	−6.70641	−	0.132797i	−0.369175	−	0.00731023i
$331$	9.12459	+	15.8042i	0.501533	+	0.868680i	0.999998	+	0.00177061i	$0.000563604\pi$
$331$	9.12459	+	15.8042i	0.501533	+	0.868680i	−0.498466	+	0.866909i	$0.666103\pi$
$332$	−5.11499	+	8.85943i	−0.280722	+	0.486224i
$333$	4.69635	−	8.13432i	0.257359	−	0.445758i
$334$	11.3565	−	6.55669i	0.621401	−	0.358766i
$335$			42.7675i			2.33664i
$336$	4.81385	+	1.14742i	0.262617	+	0.0625970i
$337$		−	31.5515i		−	1.71872i	−0.511370	−	0.859360i	$-0.670862\pi$
$337$		−	31.5515i		−	1.71872i	0.511370	−	0.859360i	$-0.329138\pi$
$338$	−6.91873	+	3.99453i	−0.376329	+	0.217274i
$339$	10.2965	+	5.94468i	0.559228	+	0.322871i
$340$	33.5087	+	19.3462i	1.81726	+	1.04920i
$341$	7.71869	+	14.0022i	0.417991	+	0.758264i
$342$			0.534962i			0.0289275i
$343$	11.9591	−	14.1415i	0.645729	−	0.763567i
$344$	21.5449			1.16162
$345$	5.85386	+	10.1392i	0.315161	+	0.545875i
$346$	−0.797991	−	0.460721i	−0.0429003	−	0.0247685i
$347$	−14.1061	−	8.14414i	−0.757253	−	0.437200i	0.0710553	−	0.997472i	$-0.477363\pi$
$347$	−14.1061	−	8.14414i	−0.757253	−	0.437200i	−0.828309	+	0.560272i	$0.810697\pi$
$348$	−3.00430	−	5.20359i	−0.161047	−	0.278942i
$349$	16.8476			0.901829			0.450915	−	0.892567i	$-0.351098\pi$
$349$	16.8476			0.901829			0.450915	+	0.892567i	$0.351098\pi$
$350$	9.18258	+	2.18875i	0.490830	+	0.116993i
$351$			0.142630i			0.00761300i
$352$	8.98062	+	16.2915i	0.478669	+	0.868338i
$353$	8.72575	+	5.03782i	0.464425	+	0.268136i	0.713903	−	0.700245i	$-0.246926\pi$
$353$	8.72575	+	5.03782i	0.464425	+	0.268136i	−0.249478	+	0.968380i	$0.580259\pi$
$354$	−0.824643	−	0.476108i	−0.0438293	−	0.0253049i
$355$	7.58448	−	4.37890i	0.402542	−	0.232408i
$356$			12.7725i			0.676939i
$357$	5.48815	+	18.4176i	0.290464	+	0.974762i
$358$		−	9.43359i		−	0.498581i
$359$	−11.6509	+	6.72664i	−0.614910	+	0.355018i	−0.774885	−	0.632103i	$-0.782192\pi$
$359$	−11.6509	+	6.72664i	−0.614910	+	0.355018i	0.159975	+	0.987121i	$0.448859\pi$
$360$	−3.66181	+	6.34243i	−0.192994	+	0.334276i
$361$	9.12230	−	15.8003i	0.480121	−	0.831594i
$362$	−4.49105	−	7.77872i	−0.236044	−	0.408841i
$363$	−0.435462	+	10.9914i	−0.0228558	+	0.576898i
$364$	−0.444441	−	0.420386i	−0.0232950	−	0.0220342i
$365$			18.0339i			0.943938i
$366$	4.69413	+	8.13047i	0.245366	+	0.424986i
$367$	−15.8894	−	9.17373i	−0.829418	−	0.478865i	0.0242354	−	0.999706i	$-0.492285\pi$
$367$	−15.8894	−	9.17373i	−0.829418	−	0.478865i	−0.853653	+	0.520842i	$0.825618\pi$
$368$	3.33226	−	5.77165i	0.173706	−	0.300868i
$369$	−1.59743	−	2.76684i	−0.0831590	−	0.144036i
$370$	−18.9963			−0.987571
$371$	12.7348	+	12.0455i	0.661156	+	0.625372i
$372$	7.81525			0.405202
$373$	−20.9396	+	12.0895i	−1.08421	+	0.625970i	−0.932030	−	0.362382i	$-0.881964\pi$
$373$	−20.9396	+	12.0895i	−1.08421	+	0.625970i	−0.152183	+	0.988352i	$0.548630\pi$
$374$	−7.66683	+	12.6922i	−0.396442	+	0.656299i
$375$	1.30895	−	2.26717i	0.0675940	−	0.117076i
$376$	−9.76564	−	16.9146i	−0.503625	−	0.872303i
$377$			0.528638i			0.0272263i
$378$	−1.56066	+	0.465052i	−0.0802717	+	0.0239197i
$379$	17.5684			0.902427			0.451214	−	0.892416i	$-0.350991\pi$
$379$	17.5684			0.902427			0.451214	+	0.892416i	$0.350991\pi$
$380$	−4.00951	+	2.31489i	−0.205683	+	0.118751i
$381$	−7.84106	+	13.5811i	−0.401710	+	0.695781i
$382$	4.78227	+	2.76104i	0.244682	+	0.141267i
$383$	9.83515	−	5.67833i	0.502553	−	0.290149i	−0.227214	−	0.973845i	$-0.572962\pi$
$383$	9.83515	−	5.67833i	0.502553	−	0.290149i	0.729767	+	0.683696i	$0.239628\pi$
$384$	11.3955			0.581524
$385$	7.23929	−	27.9095i	0.368948	−	1.42240i
$386$	−1.29995			−0.0661655
$387$	8.37136	−	4.83321i	0.425540	−	0.245686i
$388$	−11.3327	−	6.54291i	−0.575328	−	0.332166i
$389$	−0.0981512	+	0.170003i	−0.00497646	+	0.00861949i	−0.868503	−	0.495684i	$-0.834917\pi$
$389$	−0.0981512	+	0.170003i	−0.00497646	+	0.00861949i	0.863526	+	0.504304i	$0.168251\pi$
$390$	0.249815	−	0.144231i	0.0126499	−	0.00730341i
$391$	25.8811			1.30886
$392$	7.03784	−	13.9244i	0.355464	−	0.703287i
$393$		−	10.0286i		−	0.505874i
$394$	−2.91718	−	5.05271i	−0.146966	−	0.254552i
$395$	11.5883	−	20.0715i	0.583069	−	1.00991i
$396$	4.60227	+	2.78004i	0.231273	+	0.139702i
$397$	−10.1258	+	5.84613i	−0.508199	+	0.293409i	−0.732093	−	0.681204i	$-0.761456\pi$
$397$	−10.1258	+	5.84613i	−0.508199	+	0.293409i	0.223894	+	0.974614i	$0.428123\pi$
$398$	0.820241			0.0411150
$399$	−2.23687	−	0.533177i	−0.111983	−	0.0266922i
$400$	−10.8424			−0.542120
$401$	−14.1112	−	24.4413i	−0.704680	−	1.22054i	−0.966807	−	0.255508i	$-0.917757\pi$
$401$	−14.1112	−	24.4413i	−0.704680	−	1.22054i	0.262127	−	0.965033i	$-0.415576\pi$
$402$	−4.00563	+	6.93795i	−0.199782	+	0.346033i
$403$	−0.595469	−	0.343794i	−0.0296624	−	0.0171256i
$404$	−5.58979	−	9.68180i	−0.278102	−	0.481687i
$405$			3.28584i			0.163275i
$406$	−5.78439	+	1.72366i	−0.287075	+	0.0855437i
$407$	−0.616737	+	31.1460i	−0.0305705	+	1.54385i
$408$	8.09480	+	14.0206i	0.400752	+	0.694123i
$409$	−10.2854	+	17.8149i	−0.508581	+	0.880888i	0.491370	+	0.870951i	$0.336496\pi$
$409$	−10.2854	+	17.8149i	−0.508581	+	0.880888i	−0.999951	+	0.00993696i	$0.996837\pi$
$410$	−3.23073	+	5.59580i	−0.159555	+	0.276357i
$411$	−12.7119	+	7.33923i	−0.627033	+	0.362018i
$412$			5.60941i			0.276356i
$413$	2.81267	−	2.97361i	0.138402	−	0.146322i
$414$			2.19310i			0.107785i
$415$	17.9568	−	10.3673i	0.881463	−	0.508913i
$416$	−0.692822	−	0.400001i	−0.0339684	−	0.0196117i
$417$	3.85843	+	2.22767i	0.188948	+	0.109089i
$418$	−0.856541	−	1.55382i	−0.0418948	−	0.0760001i
$419$		−	24.6522i		−	1.20434i	−0.798368	−	0.602170i	$-0.794303\pi$
$419$		−	24.6522i		−	1.20434i	0.798368	−	0.602170i	$-0.205697\pi$
$420$	−10.2388	−	9.68468i	−0.499604	−	0.472564i
$421$	28.5775			1.39278			0.696391	−	0.717663i	$-0.254788\pi$
$421$	28.5775			1.39278			0.696391	+	0.717663i	$0.254788\pi$
$422$	−1.64427	−	2.84795i	−0.0800416	−	0.138636i
$423$	−7.58896	−	4.38149i	−0.368988	−	0.213035i
$424$	12.7885	+	7.38345i	0.621065	+	0.358572i
$425$	−21.0528	−	36.4645i	−1.02121	−	1.76879i
$426$	1.64052			0.0794835
$427$	−38.6748	+	11.5245i	−1.87161	+	0.557709i
$428$			3.43909i			0.166235i
$429$	−0.228367	−	0.414274i	−0.0110257	−	0.0200014i
$430$	−16.9307	−	9.77494i	−0.816470	−	0.471389i
$431$	−16.4532	−	9.49927i	−0.792524	−	0.457564i	0.0483265	−	0.998832i	$-0.484611\pi$
$431$	−16.4532	−	9.49927i	−0.792524	−	0.457564i	−0.840850	+	0.541268i	$0.817945\pi$
$432$	1.61985	−	0.935219i	0.0779349	−	0.0449957i
$433$		−	13.5205i		−	0.649755i	−0.945756	−	0.324878i	$-0.894677\pi$
$433$		−	13.5205i		−	0.649755i	0.945756	−	0.324878i	$-0.105323\pi$
$434$	1.82025	−	7.63662i	0.0873750	−	0.366570i
$435$			12.1785i			0.583916i
$436$	4.52715	−	2.61375i	0.216811	−	0.125176i
$437$	−1.54841	+	2.68193i	−0.0740706	+	0.128294i
$438$	−1.68907	+	2.92555i	−0.0807067	+	0.139788i
$439$	−1.20494	−	2.08703i	−0.0575089	−	0.0996083i	0.835838	−	0.548977i	$-0.184982\pi$
$439$	−1.20494	−	2.08703i	−0.0575089	−	0.0996083i	−0.893347	+	0.449368i	$0.851649\pi$
$440$	0.480878	−	24.2849i	0.0229250	−	1.15774i
$441$	−0.389098	−	6.98918i	−0.0185285	−	0.332818i
$442$		−	0.637674i		−	0.0303311i
$443$	−11.8597	−	20.5416i	−0.563470	−	0.975959i	−0.997190	−	0.0749112i	$-0.976133\pi$
$443$	−11.8597	−	20.5416i	−0.563470	−	0.975959i	0.433720	−	0.901048i	$-0.357201\pi$
$444$	13.1870	+	7.61350i	0.625826	+	0.361321i
$445$	12.9440	−	22.4196i	0.613602	−	1.06279i
$446$	7.54947	+	13.0761i	0.357478	+	0.619170i
$447$	5.01591			0.237245
$448$	−0.176999	+	0.742574i	−0.00836240	+	0.0350833i
$449$	−0.0666558			−0.00314568			−0.00157284	−	0.999999i	$-0.500501\pi$
$449$	−0.0666558			−0.00314568			−0.00157284	+	0.999999i	$0.500501\pi$
$450$	3.08991	−	1.78396i	0.145660	−	0.0840967i
$451$	9.06987	+	5.47872i	0.427083	+	0.257983i
$452$	−9.63722	+	16.6922i	−0.453297	+	0.785133i
$453$	−7.36619	−	12.7586i	−0.346094	−	0.599452i
$454$			8.09811i			0.380063i
$455$	0.354099	+	1.18831i	0.0166004	+	0.0557091i
$456$	−1.93718			−0.0907168
$457$	−26.9517	+	15.5606i	−1.26075	+	0.727892i	−0.973219	−	0.229881i	$-0.926166\pi$
$457$	−26.9517	+	15.5606i	−1.26075	+	0.727892i	−0.287527	+	0.957773i	$0.592833\pi$
$458$	4.32724	−	7.49500i	0.202199	−	0.350218i
$459$	6.29053	+	3.63184i	0.293617	+	0.169520i
$460$	−16.4371	+	9.48999i	−0.766386	+	0.442473i
$461$	−3.58542			−0.166990			−0.0834948	−	0.996508i	$-0.526608\pi$
$461$	−3.58542			−0.166990			−0.0834948	+	0.996508i	$0.526608\pi$
$462$	3.78841	−	3.84958i	0.176253	−	0.179099i
$463$	−20.7914			−0.966260			−0.483130	−	0.875549i	$-0.660500\pi$
$463$	−20.7914			−0.966260			−0.483130	+	0.875549i	$0.660500\pi$
$464$	6.00375	−	3.46627i	0.278717	−	0.160917i
$465$	−13.7182	−	7.92018i	−0.636164	−	0.367290i
$466$	−7.95569	+	13.7797i	−0.368540	+	0.638331i
$467$	33.6679	−	19.4382i	1.55796	−	0.899491i	0.560513	−	0.828146i	$-0.310604\pi$
$467$	33.6679	−	19.4382i	1.55796	−	0.899491i	0.997452	−	0.0713455i	$-0.0227293\pi$
$468$	−0.231224			−0.0106883
$469$	−25.0178	−	23.6637i	−1.15521	−	1.09269i
$470$			17.7227i			0.817488i
$471$	−5.18336	−	8.97784i	−0.238837	−	0.413677i
$472$	1.72406	−	2.98616i	0.0793563	−	0.137449i
$473$	−16.5765	+	27.4419i	−0.762187	+	1.26178i
$474$	3.75981	−	2.17073i	0.172694	−	0.0997048i
$475$	5.03818			0.231167
$476$	−29.8577	+	8.89713i	−1.36853	+	0.407799i
$477$	6.62537			0.303355
$478$	2.30555	+	3.99333i	0.105453	+	0.182651i
$479$	8.07956	−	13.9942i	0.369164	−	0.639412i	−0.620271	−	0.784388i	$-0.712977\pi$
$479$	8.07956	−	13.9942i	0.369164	−	0.639412i	0.989435	+	0.144976i	$0.0463106\pi$
$480$	−15.9609	−	9.21505i	−0.728514	−	0.420607i
$481$	−0.669839	−	1.16019i	−0.0305420	−	0.0529003i
$482$			11.1758i			0.509046i
$483$	−9.17013	−	2.18578i	−0.417256	−	0.0994564i
$484$	−17.8187	−	0.705951i	−0.809941	−	0.0320887i
$485$	13.2615	+	22.9696i	0.602174	+	1.04300i
$486$	−0.307753	+	0.533044i	−0.0139600	+	0.0241794i
$487$	0.0236137	−	0.0409002i	0.00107004	−	0.00185336i	−0.865490	−	0.500926i	$-0.832993\pi$
$487$	0.0236137	−	0.0409002i	0.00107004	−	0.00185336i	0.866560	+	0.499073i	$0.166326\pi$
$488$	−29.4417	+	16.9981i	−1.33276	+	0.769470i
$489$			6.22238i			0.281386i
$490$	−11.8481	+	7.74915i	−0.535240	+	0.350071i
$491$		−	30.2054i		−	1.36315i	−0.731748	−	0.681576i	$-0.761295\pi$
$491$		−	30.2054i		−	1.36315i	0.731748	−	0.681576i	$-0.238705\pi$
$492$	4.48546	−	2.58968i	0.202220	−	0.116752i
$493$	23.3151	+	13.4610i	1.05006	+	0.606251i
$494$	0.0660790	+	0.0381507i	0.00297303	+	0.00171648i
$495$	−5.26103	−	9.54387i	−0.236466	−	0.428965i
$496$			9.01700i			0.404875i
$497$	−1.63504	+	6.85960i	−0.0733418	+	0.307695i
$498$	3.88404			0.174048
$499$	−0.754669	−	1.30713i	−0.0337836	−	0.0585150i	0.848639	−	0.528972i	$-0.177422\pi$
$499$	−0.754669	−	1.30713i	−0.0337836	−	0.0585150i	−0.882423	+	0.470457i	$0.844089\pi$
$500$	3.67543	+	2.12201i	0.164370	+	0.0948992i
$501$	18.4507	+	10.6525i	0.824316	+	0.475919i
$502$	−0.946321	−	1.63908i	−0.0422364	−	0.0731555i
$503$	37.3354			1.66471			0.832353	−	0.554247i	$-0.186994\pi$
$503$	37.3354			1.66471			0.832353	+	0.554247i	$0.186994\pi$
$504$	−1.68403	−	5.65139i	−0.0750124	−	0.251733i
$505$			22.6594i			1.00833i
$506$	−3.51142	−	6.36997i	−0.156102	−	0.283180i
$507$	−11.2407	−	6.48983i	−0.499218	−	0.288223i
$508$	−22.0170	−	12.7115i	−0.976848	−	0.563984i
$509$	−9.41068	+	5.43326i	−0.417121	+	0.240825i	−0.693845	−	0.720124i	$-0.744085\pi$
$509$	−9.41068	+	5.43326i	−0.417121	+	0.240825i	0.276724	+	0.960950i	$0.410751\pi$
$510$		−	14.6905i		−	0.650505i
$511$	−10.5493	−	9.97836i	−0.466675	−	0.441417i
$512$			18.8290i			0.832132i
$513$	−0.752699	+	0.434571i	−0.0332325	+	0.0191868i
$514$	−1.07337	+	1.85914i	−0.0473445	+	0.0820031i
$515$	5.68473	−	9.84624i	0.250499	−	0.433877i
$516$	7.83536	+	13.5712i	0.344933	+	0.597441i
$517$	29.0578	+	0.575388i	1.27796	+	0.0253055i
$518$	10.5109	−	11.1123i	0.461821	−	0.488247i
$519$		−	1.49705i		−	0.0657130i
$520$	0.522282	+	0.904618i	0.0229036	+	0.0396701i
$521$	−15.4303	−	8.90869i	−0.676014	−	0.390297i	0.122338	−	0.992489i	$-0.460961\pi$
$521$	−15.4303	−	8.90869i	−0.676014	−	0.390297i	−0.798351	+	0.602192i	$0.794294\pi$
$522$	−1.14065	+	1.97566i	−0.0499248	+	0.0864723i
$523$	16.1881	+	28.0387i	0.707858	+	1.22605i	0.965650	+	0.259845i	$0.0836716\pi$
$523$	16.1881	+	28.0387i	0.707858	+	1.22605i	−0.257792	+	0.966200i	$0.582995\pi$
$524$	16.2578			0.710227
$525$	4.37978	+	14.6980i	0.191149	+	0.641474i
$526$	−3.97787			−0.173443
$527$	−30.3254	+	17.5084i	−1.32100	+	0.762677i
$528$	−3.20752	+	5.30996i	−0.139589	+	0.231086i
$529$	5.15222	−	8.92390i	0.224009	−	0.387996i
$530$	−6.69975	−	11.6043i	−0.291019	−	0.504059i
$531$		−	1.54704i		−	0.0671360i
$532$	0.864360	−	3.62630i	0.0374748	−	0.157220i
$533$	−0.455682			−0.0197378
$534$	4.19966	−	2.42468i	0.181737	−	0.104926i
$535$	3.48527	−	6.03666i	0.150681	−	0.260988i
$536$	−25.1234	−	14.5050i	−1.08516	−	0.626520i
$537$	13.2732	−	7.66328i	0.572780	−	0.330695i
$538$	10.1836			0.439045
$539$	12.3207	+	19.6774i	0.530690	+	0.847566i
$540$	−5.32684			−0.229231
$541$	21.4681	−	12.3946i	0.922986	−	0.532886i	0.0383994	−	0.999262i	$-0.487774\pi$
$541$	21.4681	−	12.3946i	0.922986	−	0.532886i	0.884586	+	0.466376i	$0.154441\pi$
$542$	−2.15189	−	1.24240i	−0.0924317	−	0.0533655i
$543$	7.29651	−	12.6379i	0.313123	−	0.542345i
$544$	−35.2833	+	20.3708i	−1.51276	+	0.873392i
$545$	−10.5954			−0.453856
$546$	−0.0538545	+	0.225939i	−0.00230476	+	0.00966931i
$547$			15.2233i			0.650903i	0.945559	+	0.325452i	$0.105516\pi$
$547$			15.2233i			0.650903i	−0.945559	+	0.325452i	$0.894484\pi$
$548$	−11.8980	−	20.6080i	−0.508258	−	0.880329i
$549$	−7.62645	+	13.2094i	−0.325489	+	0.563763i
$550$	−6.11846	+	10.1289i	−0.260892	+	0.431899i
$551$	−2.78978	+	1.61068i	−0.118849	+	0.0686174i
$552$	−7.94155			−0.338015
$553$	5.32932	+	17.8846i	0.226626	+	0.760530i
$554$	1.50717			0.0640337
$555$	−15.4315	−	26.7281i	−0.655029	−	1.13454i
$556$	−3.61139	+	6.25511i	−0.153157	+	0.265276i
$557$	−19.1385	−	11.0496i	−0.810924	−	0.468187i	0.0363526	−	0.999339i	$-0.488426\pi$
$557$	−19.1385	−	11.0496i	−0.810924	−	0.468187i	−0.847277	+	0.531152i	$0.821759\pi$
$558$	−1.48362	−	2.56970i	−0.0628065	−	0.108784i
$559$		−	1.37872i		−	0.0583135i
$560$	11.1739	−	11.8133i	0.472183	−	0.499201i
$561$	−24.0862	−	0.476943i	−1.01692	−	0.0201365i
$562$	−4.36704	−	7.56393i	−0.184212	−	0.319065i
$563$	12.9555	−	22.4396i	0.546009	−	0.945716i	−0.452533	−	0.891747i	$-0.649480\pi$
$563$	12.9555	−	22.4396i	0.546009	−	0.945716i	0.998543	−	0.0539682i	$-0.0171870\pi$
$564$	7.10306	−	12.3029i	0.299093	−	0.518044i
$565$	33.8326	−	19.5332i	1.42335	−	0.821769i
$566$			16.4221i			0.690270i
$567$	−1.92212	−	1.81809i	−0.0807215	−	0.0763526i
$568$			5.94058i			0.249261i
$569$	25.6436	−	14.8053i	1.07504	−	0.620672i	0.145483	−	0.989361i	$-0.453526\pi$
$569$	25.6436	−	14.8053i	1.07504	−	0.620672i	0.929553	+	0.368689i	$0.120193\pi$
$570$	1.52230	+	0.878900i	0.0637621	+	0.0368131i
$571$	−7.21178	−	4.16372i	−0.301804	−	0.174246i	0.341449	−	0.939900i	$-0.389082\pi$
$571$	−7.21178	−	4.16372i	−0.301804	−	0.174246i	−0.643253	+	0.765654i	$0.722416\pi$
$572$	0.671602	−	0.370218i	0.0280811	−	0.0154796i
$573$			8.97161i			0.374795i
$574$	−1.48578	−	4.98610i	−0.0620153	−	0.208116i
$575$	20.6542			0.861340
$576$	0.144265	+	0.249874i	0.00601103	+	0.0104114i
$577$	−24.7495	−	14.2891i	−1.03033	−	0.594864i	−0.113254	−	0.993566i	$-0.536127\pi$
$577$	−24.7495	−	14.2891i	−1.03033	−	0.594864i	−0.917080	+	0.398702i	$0.869461\pi$
$578$	−19.0622	−	11.0056i	−0.792884	−	0.457772i
$579$	−1.05600	−	1.82904i	−0.0438857	−	0.0760123i
$580$	−19.7433			−0.819794
$581$	−3.87108	+	16.2406i	−0.160599	+	0.673772i
$582$			4.96832i			0.205944i
$583$	−19.2437	+	10.6080i	−0.796993	+	0.439340i
$584$	−10.5939	−	6.11636i	−0.438377	−	0.253097i
$585$	0.405869	+	0.234329i	0.0167806	+	0.00968830i
$586$	9.81236	−	5.66517i	0.405345	−	0.234026i
$587$		−	26.8088i		−	1.10652i	−0.833009	−	0.553260i	$-0.813384\pi$
$587$		−	26.8088i		−	1.10652i	0.833009	−	0.553260i	$-0.186616\pi$
$588$	11.3305	−	0.630787i	0.467263	−	0.0260132i
$589$		−	4.18996i		−	0.172644i
$590$	−2.70964	+	1.56441i	−0.111554	+	0.0644059i
$591$	4.73948	−	8.20903i	0.194956	−	0.337674i
$592$	−8.78423	+	15.2147i	−0.361030	+	0.625322i
$593$	12.1833	+	21.1021i	0.500308	+	0.866558i	1.00000		0.000355423i	$0.000113135\pi$
$593$	12.1833	+	21.1021i	0.500308	+	0.866558i	−0.499692	+	0.866203i	$0.666554\pi$
$594$	0.0404149	−	2.04100i	0.00165825	−	0.0837434i
$595$	61.4260	+	14.6414i	2.51822	+	0.600240i
$596$			8.13156i			0.333082i
$597$	0.666314	+	1.15409i	0.0272704	+	0.0472337i
$598$	0.270894	+	0.156401i	0.0110777	+	0.00639569i
$599$	18.6897	−	32.3716i	0.763642	−	1.32267i	−0.177319	−	0.984153i	$-0.556742\pi$
$599$	18.6897	−	32.3716i	0.763642	−	1.32267i	0.940961	−	0.338514i	$-0.109924\pi$
$600$	6.45999	+	11.1890i	0.263728	+	0.456790i
$601$	0.423296			0.0172666			0.00863329	−	0.999963i	$-0.497252\pi$
$601$	0.423296			0.0172666			0.00863329	+	0.999963i	$0.497252\pi$
$602$	15.0860	−	4.49539i	0.614859	−	0.183218i
$603$	−13.0157			−0.530041
$604$	20.6837	−	11.9417i	0.841606	−	0.485901i
$605$	30.5618	+	19.2971i	1.24252	+	0.784539i
$606$	−2.12229	+	3.67591i	−0.0862120	+	0.149324i
$607$	−15.7564	−	27.2909i	−0.639534	−	1.10771i	−0.985535	−	0.169471i	$-0.945794\pi$
$607$	−15.7564	−	27.2909i	−0.639534	−	1.10771i	0.346001	−	0.938234i	$-0.387539\pi$
$608$		−	4.87497i		−	0.197706i
$609$	−7.12410	−	6.73852i	−0.288683	−	0.273059i
$610$	30.8483			1.24901
$611$	−1.08241	+	0.624929i	−0.0437896	+	0.0252819i
$612$	−5.88777	+	10.1979i	−0.237999	+	0.412226i
$613$	24.2895	+	14.0235i	0.981042	+	0.566405i	0.902585	−	0.430512i	$-0.141667\pi$
$613$	24.2895	+	14.0235i	0.981042	+	0.566405i	0.0784577	+	0.996917i	$0.475000\pi$
$614$	−12.9243	+	7.46185i	−0.521582	+	0.301136i
$615$	−10.4978			−0.423313
$616$	13.9399	+	13.7184i	0.561655	+	0.552731i
$617$	−41.4810			−1.66996			−0.834981	−	0.550279i	$-0.814521\pi$
$617$	−41.4810			−1.66996			−0.834981	+	0.550279i	$0.814521\pi$
$618$	1.84441	−	1.06487i	0.0741930	−	0.0428353i
$619$	9.29533	+	5.36666i	0.373611	+	0.215704i	0.675035	−	0.737786i	$-0.264129\pi$
$619$	9.29533	+	5.36666i	0.373611	+	0.215704i	−0.301424	+	0.953490i	$0.597462\pi$
$620$	12.8398	−	22.2392i	0.515659	−	0.893148i
$621$	−3.08572	+	1.78154i	−0.123826	+	0.0714908i
$622$	7.71610			0.309387
$623$	5.95279	+	19.9769i	0.238493	+	0.800356i
$624$		−	0.266780i		−	0.0106797i
$625$	10.1908	+	17.6510i	0.407632	+	0.706040i
$626$	−2.94261	+	5.09675i	−0.117610	+	0.203707i
$627$	1.49045	−	2.46740i	0.0595228	−	0.0985383i
$628$	14.5544	−	8.40301i	0.580786	−	0.335317i
$629$	−68.2256			−2.72033
$630$	−1.24068	+	5.20509i	−0.0494298	+	0.207376i
$631$	3.36006			0.133762			0.0668809	−	0.997761i	$-0.478695\pi$
$631$	3.36006			0.133762			0.0668809	+	0.997761i	$0.478695\pi$
$632$	7.86054	+	13.6148i	0.312675	+	0.541570i
$633$	2.67140	−	4.62701i	0.106179	−	0.183907i
$634$	7.37151	+	4.25594i	0.292760	+	0.169025i
$635$	25.7644	+	44.6253i	1.02243	+	1.77090i
$636$			10.7407i			0.425898i
$637$	−0.891057	−	0.450370i	−0.0353050	−	0.0178443i
$638$	0.149793	−	7.56472i	0.00593036	−	0.299490i
$639$	1.33266	+	2.30823i	0.0527192	+	0.0913123i
$640$	18.7219	−	32.4272i	0.740047	−	1.28180i
$641$	−16.8337	+	29.1568i	−0.664890	+	1.15162i	0.314425	+	0.949282i	$0.398188\pi$
$641$	−16.8337	+	29.1568i	−0.664890	+	1.15162i	−0.979315	+	0.202341i	$0.935145\pi$
$642$	1.13079	−	0.652864i	0.0446289	−	0.0257665i
$643$			37.8334i			1.49200i	0.665944	+	0.746002i	$0.268029\pi$
$643$			37.8334i			1.49200i	−0.665944	+	0.746002i	$0.731971\pi$
$644$	3.54348	−	14.8662i	0.139633	−	0.585810i
$645$		−	31.7623i		−	1.25064i
$646$	3.36520	−	1.94290i	0.132402	−	0.0764423i
$647$	−4.35026	−	2.51162i	−0.171026	−	0.0987421i	0.412043	−	0.911164i	$-0.364815\pi$
$647$	−4.35026	−	2.51162i	−0.171026	−	0.0987421i	−0.583070	+	0.812422i	$0.698149\pi$
$648$	−1.93023	−	1.11442i	−0.0758268	−	0.0437786i
$649$	2.47701	+	4.49347i	0.0972311	+	0.176384i
$650$		−	0.508891i		−	0.0199603i
$651$	12.2235	−	3.64241i	0.479076	−	0.142757i
$652$	−10.0874			−0.395054
$653$	15.8588	+	27.4682i	0.620601	+	1.07491i	0.989374	+	0.145393i	$0.0464447\pi$
$653$	15.8588	+	27.4682i	0.620601	+	1.07491i	−0.368773	+	0.929520i	$0.620222\pi$
$654$	−1.71883	−	0.992368i	−0.0672116	−	0.0388047i
$655$	−28.5375	−	16.4761i	−1.11505	−	0.643775i
$656$	2.98790	+	5.17519i	0.116658	+	0.202057i
$657$	−5.48838			−0.214122
$658$	−10.3673	−	9.80617i	−0.404159	−	0.382284i
$659$		−	3.15699i		−	0.122979i	−0.998108	−	0.0614894i	$-0.980415\pi$
$659$		−	3.15699i		−	0.122979i	0.998108	−	0.0614894i	$-0.0195851\pi$
$660$	15.4721	−	8.52893i	0.602249	−	0.331988i
$661$	38.5175	+	22.2381i	1.49816	+	0.864962i	0.999998	−	0.00212278i	$-0.000675703\pi$
$661$	38.5175	+	22.2381i	1.49816	+	0.864962i	0.498160	+	0.867085i	$0.334009\pi$
$662$	9.72762	+	5.61624i	0.378075	+	0.218281i
$663$	0.897216	−	0.518008i	0.0348450	−	0.0201178i
$664$			14.0647i			0.545816i
$665$	−5.19221	+	5.48931i	−0.201345	+	0.212866i
$666$		−	5.78127i		−	0.224020i
$667$	−11.4368	+	6.60306i	−0.442836	+	0.255671i
$668$	−17.2693	+	29.9114i	−0.668171	+	1.15731i
$669$	−12.2655	+	21.2444i	−0.474210	+	0.821356i
$670$	13.1618	+	22.7970i	0.508486	+	0.880724i
$671$	1.00152	−	50.5782i	0.0386634	−	1.95255i
$672$	14.2219	−	4.23790i	0.548622	−	0.163481i
$673$		−	29.7473i		−	1.14667i	−0.819319	−	0.573337i	$-0.805648\pi$
$673$		−	29.7473i		−	1.14667i	0.819319	−	0.573337i	$-0.194352\pi$
$674$	−9.71008	−	16.8184i	−0.374018	−	0.647819i
$675$	5.02011	+	2.89836i	0.193224	+	0.111558i
$676$	10.5210	−	18.2229i	0.404654	−	0.700881i
$677$	−7.16801	−	12.4154i	−0.275489	−	0.477161i	0.694769	−	0.719233i	$-0.255506\pi$
$677$	−7.16801	−	12.4154i	−0.275489	−	0.477161i	−0.970258	+	0.242071i	$0.922173\pi$
$678$	7.31797			0.281045
$679$	−20.7743	−	4.95174i	−0.797245	−	0.190030i
$680$	53.1964			2.03999
$681$	−11.3941	+	6.57841i	−0.436625	+	0.252085i
$682$	8.42364	+	5.08836i	0.322558	+	0.194844i
$683$	−7.14207	+	12.3704i	−0.273284	+	0.473341i	−0.969701	−	0.244296i	$-0.921443\pi$
$683$	−7.14207	+	12.3704i	−0.273284	+	0.473341i	0.696417	+	0.717637i	$0.254776\pi$
$684$	−0.704506	−	1.22024i	−0.0269374	−	0.0466570i
$685$			48.2311i			1.84281i
$686$	2.02263	−	11.2185i	0.0772243	−	0.428323i
$687$	14.0607			0.536451
$688$	−15.6581	+	9.04021i	−0.596959	+	0.344655i
$689$	0.472487	−	0.818371i	0.0180003	−	0.0311775i
$690$	6.24073	+	3.60309i	0.237580	+	0.137167i
$691$	17.8180	−	10.2872i	0.677830	−	0.391345i	−0.121207	−	0.992627i	$-0.538676\pi$
$691$	17.8180	−	10.2872i	0.677830	−	0.391345i	0.799037	+	0.601282i	$0.205343\pi$
$692$	2.42694			0.0922583
$693$	8.49388	+	2.20318i	0.322656	+	0.0836919i
$694$	−10.0255			−0.380564
$695$	12.6782	−	7.31975i	0.480911	−	0.277654i
$696$	−7.15417	−	4.13046i	−0.271178	−	0.156565i
$697$	−11.6032	+	20.0974i	−0.439504	+	0.761244i
$698$	8.98049	−	5.18489i	0.339917	−	0.196251i
$699$	−25.8509			−0.977770
$700$	−23.8277	+	7.10028i	−0.900603	+	0.268365i
$701$		−	7.46334i		−	0.281886i	−0.990018	−	0.140943i	$-0.954987\pi$
$701$		−	7.46334i		−	0.281886i	0.990018	−	0.140943i	$-0.0450135\pi$
$702$	0.0438947	+	0.0760278i	0.00165670	+	0.00286949i
$703$	4.08180	−	7.06988i	0.153948	−	0.266646i
$704$	−0.819102	−	0.494785i	−0.0308711	−	0.0186479i
$705$	−24.9361	+	14.3969i	−0.939147	+	0.542217i
$706$	6.20162			0.233401
$707$	−13.2551	−	12.5377i	−0.498509	−	0.471528i
$708$	2.50799			0.0942562
$709$	17.5066	+	30.3222i	0.657473	+	1.13878i	0.981268	+	0.192649i	$0.0617078\pi$
$709$	17.5066	+	30.3222i	0.657473	+	1.13878i	−0.323795	+	0.946127i	$0.604959\pi$
$710$	2.69524	−	4.66830i	0.101151	−	0.175198i
$711$	6.10848	+	3.52673i	0.229086	+	0.132263i
$712$	8.78012	+	15.2076i	0.329049	+	0.569929i
$713$		−	17.1769i		−	0.643280i
$714$	8.59350	+	8.12839i	0.321604	+	0.304198i
$715$	−1.55406	−	0.0307727i	−0.0581184	−	0.00115083i
$716$	12.4233	+	21.5178i	0.464282	+	0.804160i
$717$	−3.74578	+	6.48788i	−0.139889	+	0.242294i
$718$	−4.14029	+	7.17119i	−0.154514	+	0.267626i
$719$	−23.5833	+	13.6158i	−0.879508	+	0.507784i	−0.870496	−	0.492175i	$-0.836202\pi$
$719$	−23.5833	+	13.6158i	−0.879508	+	0.507784i	−0.00901198	+	0.999959i	$0.502869\pi$
$720$		−	6.14595i		−	0.229046i
$721$	2.61435	+	8.77344i	0.0973633	+	0.326740i
$722$		−	11.2297i		−	0.417925i
$723$	−15.7246	+	9.07858i	−0.584803	+	0.337636i
$724$	20.4880	+	11.8287i	0.761430	+	0.439612i
$725$	18.6064	+	10.7424i	0.691024	+	0.398963i
$726$	3.15051	+	5.99290i	0.116926	+	0.222418i
$727$		−	31.0062i		−	1.14996i	−0.818168	−	0.574979i	$-0.805010\pi$
$727$		−	31.0062i		−	1.14996i	0.818168	−	0.574979i	$-0.194990\pi$
$728$	−0.818160	−	0.195015i	−0.0303230	−	0.00722775i
$729$	−1.00000			−0.0370370
$730$	5.54999	+	9.61287i	0.205415	+	0.355788i
$731$	−60.8069	−	35.1069i	−2.24902	−	1.29847i
$732$	−21.4144	−	12.3636i	−0.791500	−	0.456973i
$733$	14.8190	+	25.6673i	0.547353	+	0.948043i	0.998455	+	0.0555703i	$0.0176977\pi$
$733$	14.8190	+	25.6673i	0.547353	+	0.948043i	−0.451102	+	0.892472i	$0.648969\pi$
$734$	−11.2930			−0.416831
$735$	−20.5278	−	10.3754i	−0.757179	−	0.382703i
$736$		−	19.9852i		−	0.736663i
$737$	37.8048	−	20.8397i	1.39256	−	0.767642i
$738$	−1.70300	−	0.983230i	−0.0626885	−	0.0361932i
$739$	−26.7820	−	15.4626i	−0.985191	−	0.568800i	−0.0813577	−	0.996685i	$-0.525926\pi$
$739$	−26.7820	−	15.4626i	−0.985191	−	0.568800i	−0.903833	+	0.427885i	$0.859259\pi$
$740$	43.3302	−	25.0167i	1.59285	−	0.919633i
$741$			0.123965i			0.00455398i
$742$	10.4952	+	2.50163i	0.385292	+	0.0918377i
$743$		−	34.4931i		−	1.26543i	−0.774385	−	0.632715i	$-0.781941\pi$
$743$		−	34.4931i		−	1.26543i	0.774385	−	0.632715i	$-0.218059\pi$
$744$	9.30527	−	5.37240i	0.341148	−	0.196962i
$745$	8.24074	−	14.2734i	0.301917	−	0.522936i
$746$	−7.44116	+	12.8885i	−0.272440	+	0.471880i
$747$	3.15516	+	5.46490i	0.115441	+	0.199950i
$748$	0.773197	−	39.0474i	0.0282709	−	1.42771i
$749$	1.60284	+	5.37893i	0.0585664	+	0.196542i
$750$		−	1.61134i		−	0.0588377i
$751$	−16.9188	−	29.3042i	−0.617376	−	1.06933i	−0.989963	−	0.141329i	$-0.954863\pi$
$751$	−16.9188	−	29.3042i	−0.617376	−	1.06933i	0.372587	−	0.927997i	$-0.378471\pi$
$752$	14.1947	+	8.19530i	0.517626	+	0.298852i
$753$	1.53747	−	2.66297i	0.0560284	−	0.0970441i
$754$	0.162690	+	0.281788i	0.00592482	+	0.0102621i
$755$	−48.4082			−1.76175
$756$	2.94740	−	3.11605i	0.107196	−	0.113330i
$757$	20.9449			0.761257			0.380628	−	0.924728i	$-0.375708\pi$
$757$	20.9449			0.761257			0.380628	+	0.924728i	$0.375708\pi$
$758$	9.36472	−	5.40673i	0.340142	−	0.196381i
$759$	6.11016	−	10.1152i	0.221785	−	0.367158i
$760$	−3.18263	+	5.51248i	−0.115446	+	0.199959i
$761$	12.9339	+	22.4022i	0.468854	+	0.812079i	0.999366	−	0.0355983i	$-0.0113337\pi$
$761$	12.9339	+	22.4022i	0.468854	+	0.812079i	−0.530512	+	0.847677i	$0.678000\pi$
$762$			9.65244i			0.349671i
$763$	5.86254	−	6.19799i	0.212238	−	0.224382i
$764$	−14.5443			−0.526196
$765$	20.6697	−	11.9336i	0.747313	−	0.431462i
$766$	3.49505	−	6.05360i	0.126281	−	0.218725i
$767$	−0.191092	−	0.110327i	−0.00689994	−	0.00398368i
$768$	5.57455	−	3.21847i	0.201154	−	0.116137i
$769$	−2.66035			−0.0959346			−0.0479673	−	0.998849i	$-0.515274\pi$
$769$	−2.66035			−0.0959346			−0.0479673	+	0.998849i	$0.515274\pi$
$770$	−4.73038	−	17.1049i	−0.170471	−	0.616418i
$771$	−3.48778			−0.125609
$772$	2.96515	−	1.71193i	0.106718	−	0.0616137i
$773$	28.8271	+	16.6433i	1.03684	+	0.598618i	0.918936	−	0.394407i	$-0.129050\pi$
$773$	28.8271	+	16.6433i	1.03684	+	0.598618i	0.117901	+	0.993025i	$0.462383\pi$
$774$	2.97487	−	5.15263i	0.106929	−	0.185207i
$775$	−24.2009	+	13.9724i	−0.869324	+	0.501904i
$776$	−17.9911			−0.645841
$777$	24.1735	+	5.76197i	0.867221	+	0.206710i
$778$			0.120825i			0.00433180i
$779$	−1.38840	−	2.40477i	−0.0497445	−	0.0861599i
$780$	−0.379882	+	0.657976i	−0.0136020	+	0.0235593i
$781$	−7.56654	−	4.57063i	−0.270752	−	0.163550i
$782$	13.7958	−	7.96499i	0.493336	−	0.284828i
$783$	−3.70637			−0.132455
$784$	0.727783	+	13.0728i	0.0259923	+	0.466886i
$785$	−34.0633			−1.21577
$786$	−3.08632	−	5.34567i	−0.110086	−	0.190674i
$787$	7.45655	−	12.9151i	0.265797	−	0.460375i	−0.701975	−	0.712202i	$-0.747698\pi$
$787$	7.45655	−	12.9151i	0.265797	−	0.460375i	0.967772	+	0.251827i	$0.0810314\pi$
$788$	13.3081	+	7.68342i	0.474081	+	0.273711i
$789$	−3.23138	−	5.59691i	−0.115040	−	0.199255i
$790$		−	14.2653i		−	0.507537i
$791$	−7.29354	+	30.5990i	−0.259329	+	1.08798i
$792$	7.39078	+	0.146349i	0.262620	+	0.00520027i
$793$	1.08776	+	1.88405i	0.0386274	+	0.0669046i
$794$	−3.59833	+	6.23250i	−0.127700	+	0.221183i
$795$	10.8849	−	18.8533i	0.386049	−	0.668657i
$796$	−1.87095	+	1.08020i	−0.0663142	+	0.0382865i
$797$			37.8391i			1.34033i	0.742212	+	0.670165i	$0.233777\pi$
$797$			37.8391i			1.34033i	−0.742212	+	0.670165i	$0.766223\pi$
$798$	−1.35644	+	0.404197i	−0.0480173	+	0.0143084i
$799$			63.6515i			2.25183i
$800$	−28.1576	+	16.2568i	−0.995520	+	0.574764i
$801$	6.82310	+	3.93932i	0.241082	+	0.139189i
$802$	−15.0438	−	8.68554i	−0.531215	−	0.306697i
$803$	15.9413	−	8.78757i	0.562555	−	0.310107i
$804$		−	21.1004i		−	0.744155i
$805$	−21.2857	+	22.5036i	−0.750222	+	0.793149i
$806$	−0.423215			−0.0149071
$807$	8.27251	+	14.3284i	0.291206	+	0.504384i
$808$	−13.3110	−	7.68513i	−0.468280	−	0.270362i
$809$	36.0225	+	20.7976i	1.26648	+	0.731204i	0.974321	−	0.225164i	$-0.0722919\pi$
$809$	36.0225	+	20.7976i	1.26648	+	0.731204i	0.292162	+	0.956369i	$0.405625\pi$
$810$	1.01123	+	1.75150i	0.0355309	+	0.0615413i
$811$	10.1870			0.357713			0.178857	−	0.983875i	$-0.442760\pi$
$811$	10.1870			0.357713			0.178857	+	0.983875i	$0.442760\pi$
$812$	10.9242	−	11.5492i	0.383363	−	0.405299i
$813$		−	4.03699i		−	0.141583i
$814$	9.25653	+	16.7920i	0.324441	+	0.588559i
$815$	17.7065	+	10.2229i	0.620232	+	0.358091i
$816$	−11.7660	−	6.79313i	−0.411894	−	0.237807i
$817$	7.27590	−	4.20074i	0.254552	−	0.146965i
$818$			12.6615i			0.442698i
$819$	−0.361648	+	0.107765i	−0.0126370	+	0.00376562i
$820$		−	17.0185i		−	0.594313i
$821$	31.1182	−	17.9661i	1.08603	−	0.627021i	0.153515	−	0.988146i	$-0.450941\pi$
$821$	31.1182	−	17.9661i	1.08603	−	0.627021i	0.932517	+	0.361126i	$0.117607\pi$
$822$	−4.51735	+	7.82427i	−0.157561	+	0.272903i
$823$	−2.32208	+	4.02195i	−0.0809425	+	0.140196i	−0.903655	−	0.428261i	$-0.859126\pi$
$823$	−2.32208	+	4.02195i	−0.0809425	+	0.140196i	0.822713	+	0.568458i	$0.192460\pi$
$824$	3.85605	+	6.67888i	0.134332	+	0.232670i
$825$	−19.2218	−	0.380620i	−0.669217	−	0.0132515i
$826$	0.584138	−	2.45067i	0.0203248	−	0.0852698i
$827$		−	28.9418i		−	1.00641i	−0.864168	−	0.503203i	$-0.832155\pi$
$827$		−	28.9418i		−	1.00641i	0.864168	−	0.503203i	$-0.167845\pi$
$828$	−2.88815	−	5.00242i	−0.100370	−	0.173846i
$829$	−5.72094	−	3.30299i	−0.198697	−	0.114717i	0.397351	−	0.917667i	$-0.369930\pi$
$829$	−5.72094	−	3.30299i	−0.198697	−	0.114717i	−0.596047	+	0.802949i	$0.703263\pi$
$830$	6.38116	−	11.0525i	0.221493	−	0.383638i
$831$	1.22434	+	2.12061i	0.0424717	+	0.0735632i
$832$	0.0411528			0.00142672
$833$	−42.5525	+	27.8312i	−1.47436	+	0.964294i
$834$	2.74229			0.0949577
$835$	60.6260	−	35.0024i	2.09805	−	1.21131i
$836$	4.00002	+	2.41625i	0.138344	+	0.0835676i
$837$	2.41040	−	4.17493i	0.0833156	−	0.144307i
$838$	−7.58681	−	13.1407i	−0.262082	−	0.453939i
$839$			10.2775i			0.354817i	0.984137	+	0.177409i	$0.0567714\pi$
$839$			10.2775i			0.354817i	−0.984137	+	0.177409i	$0.943229\pi$
$840$	−18.8484	−	4.49268i	−0.650332	−	0.155012i
$841$	15.2628			0.526304
$842$	15.2331	−	8.79481i	0.524966	−	0.303089i
$843$	7.09503	−	12.2890i	0.244366	−	0.423254i
$844$	7.50108	+	4.33075i	0.258198	+	0.149071i
$845$	−36.9351	+	21.3245i	−1.27061	+	0.733586i
$846$	−5.39367			−0.185438
$847$	−28.1985	+	7.20050i	−0.968910	+	0.247412i
$848$	−12.3923			−0.425555
$849$	−23.1060	+	13.3403i	−0.792997	+	0.457837i
$850$	−22.4441	−	12.9581i	−0.769827	−	0.444460i
$851$	16.7335	−	28.9833i	0.573617	−	0.993534i
$852$	−3.74200	+	2.16044i	−0.128199	+	0.0740156i
$853$	11.9462			0.409031			0.204516	−	0.978863i	$-0.434438\pi$
$853$	11.9462			0.409031			0.204516	+	0.978863i	$0.434438\pi$
$854$	−17.0687	+	18.0454i	−0.584079	+	0.617500i
$855$			2.85586i			0.0976683i
$856$	2.36412	+	4.09477i	0.0808039	+	0.139957i
$857$	−21.1012	+	36.5483i	−0.720802	+	1.24847i	0.239876	+	0.970804i	$0.422893\pi$
$857$	−21.1012	+	36.5483i	−0.720802	+	1.24847i	−0.960679	+	0.277663i	$0.910440\pi$
$858$	−0.249224	−	0.150546i	−0.00850838	−	0.00513955i
$859$	−35.3692	+	20.4204i	−1.20678	+	0.696735i	−0.962055	−	0.272857i	$-0.912031\pi$
$859$	−35.3692	+	20.4204i	−1.20678	+	0.696735i	−0.244726	+	0.969592i	$0.578698\pi$
$860$	51.4914			1.75584
$861$	5.80855	−	6.14092i	0.197955	−	0.209282i
$862$	−11.6937			−0.398290
$863$	2.62425	+	4.54534i	0.0893307	+	0.154725i	0.907228	−	0.420638i	$-0.138194\pi$
$863$	2.62425	+	4.54534i	0.0893307	+	0.154725i	−0.817898	+	0.575364i	$0.804861\pi$
$864$	2.80448	−	4.85749i	0.0954102	−	0.165255i
$865$	−4.26002	−	2.45952i	−0.144845	−	0.0836263i
$866$	−4.16099	−	7.20704i	−0.141396	−	0.244905i
$867$		−	35.7611i		−	1.21451i
$868$	5.90489	+	19.8161i	0.200425	+	0.672603i
$869$	−23.3891	−	0.463140i	−0.793422	−	0.0157109i
$870$	3.74798	+	6.49170i	0.127069	+	0.220089i
$871$	−0.928212	+	1.60771i	−0.0314513	+	0.0544752i
$872$	3.59352	−	6.22415i	0.121692	−	0.210776i
$873$	−6.99049	+	4.03596i	−0.236592	+	0.136597i
$874$			1.90612i			0.0644753i
$875$	6.73757	+	1.60596i	0.227772	+	0.0542913i
$876$		−	8.89749i		−	0.300618i
$877$	8.42348	−	4.86330i	0.284441	−	0.164222i	−0.350991	−	0.936379i	$-0.614155\pi$
$877$	8.42348	−	4.86330i	0.284441	−	0.164222i	0.635432	+	0.772157i	$0.280822\pi$
$878$	−1.28458	−	0.741651i	−0.0433524	−	0.0250295i
$879$	15.9419	+	9.20408i	0.537708	+	0.310446i
$880$	9.84042	+	17.8512i	0.331721	+	0.601764i
$881$			16.1119i			0.542824i	0.962463	+	0.271412i	$0.0874906\pi$
$881$			16.1119i			0.542824i	−0.962463	+	0.271412i	$0.912509\pi$
$882$	−2.35835	−	3.60579i	−0.0794097	−	0.121413i
$883$	−4.01412			−0.135086			−0.0675430	−	0.997716i	$-0.521516\pi$
$883$	−4.01412			−0.135086			−0.0675430	+	0.997716i	$0.521516\pi$
$884$	0.839769	+	1.45452i	0.0282445	+	0.0489209i
$885$	−4.40230	−	2.54167i	−0.147982	−	0.0854373i
$886$	−12.6435	−	7.29971i	−0.424765	−	0.245238i
$887$	14.1061	+	24.4326i	0.473638	+	0.820365i	0.999545	−	0.0301775i	$-0.00960724\pi$
$887$	14.1061	+	24.4326i	0.473638	+	0.820365i	−0.525907	+	0.850542i	$0.676274\pi$
$888$	20.9349			0.702528
$889$	−40.3603	−	9.62022i	−1.35364	−	0.322652i
$890$		−	15.9342i		−	0.534115i
$891$	2.90455	−	1.60112i	0.0973061	−	0.0536396i
$892$	−34.4404	−	19.8842i	−1.15315	−	0.665772i
$893$	−6.59588	−	3.80813i	−0.220723	−	0.127434i
$894$	2.67370	−	1.54366i	0.0894220	−	0.0516278i
$895$		−	50.3606i		−	1.68337i
$896$	8.60998	+	28.8941i	0.287639	+	0.965284i
$897$			0.508201i			0.0169683i
$898$	−0.0355305	+	0.0205135i	−0.00118567	+	0.000684546i
$899$	8.93384	−	15.4739i	0.297960	−	0.516082i
$900$	−4.69869	+	8.13836i	−0.156623	+	0.271279i
$901$	−24.0623	−	41.6771i	−0.801631	−	1.38847i
$902$	6.52073	+	0.129120i	0.217117	+	0.00429924i
$903$	18.5800	+	17.5744i	0.618304	+	0.584840i
$904$			26.4995i			0.881360i
$905$	−23.9751	−	41.5262i	−0.796960	−	1.38038i
$906$	−7.85301	−	4.53394i	−0.260899	−	0.150630i
$907$	3.60878	−	6.25060i	0.119828	−	0.207548i	−0.799872	−	0.600171i	$-0.795099\pi$
$907$	3.60878	−	6.25060i	0.119828	−	0.207548i	0.919699	+	0.392624i	$0.128432\pi$
$908$	−10.6646	−	18.4716i	−0.353917	−	0.613003i
$909$	−6.89607			−0.228728
$910$	0.554458	+	0.524449i	0.0183801	+	0.0173853i
$911$	−15.0138			−0.497431			−0.248715	−	0.968577i	$-0.580008\pi$
$911$	−15.0138			−0.497431			−0.248715	+	0.968577i	$0.580008\pi$
$912$	1.40788	−	0.812838i	0.0466194	−	0.0269157i
$913$	−17.9143	−	10.8213i	−0.592876	−	0.358132i
$914$	−9.57762	+	16.5889i	−0.316800	+	0.548713i
$915$	25.0593	+	43.4039i	0.828434	+	1.43489i
$916$			22.7946i			0.753155i
$917$	25.4282	−	7.57719i	0.839712	−	0.250221i
$918$	4.47084			0.147560
$919$	16.2513	−	9.38270i	0.536081	−	0.309507i	−0.207408	−	0.978255i	$-0.566503\pi$
$919$	16.2513	−	9.38270i	0.536081	−	0.309507i	0.743489	+	0.668748i	$0.233169\pi$
$920$	−13.0473	+	22.5986i	−0.430157	+	0.745055i
$921$	−20.9978	−	12.1231i	−0.691902	−	0.399470i
$922$	−1.91119	+	1.10342i	−0.0629416	+	0.0363393i
$923$	0.380153			0.0125129
$924$	−3.57169	+	13.7699i	−0.117500	+	0.452995i
$925$	−54.4469			−1.79020
$926$	−11.0828	+	6.39863i	−0.364202	+	0.210272i
$927$	2.99657	+	1.73007i	0.0984203	+	0.0568230i
$928$	10.3944	−	18.0037i	0.341214	−	0.591000i
$929$	0.992313	−	0.572912i	0.0325567	−	0.0187966i	−0.483633	−	0.875271i	$-0.660683\pi$
$929$	0.992313	−	0.572912i	0.0325567	−	0.0187966i	0.516190	+	0.856474i	$0.327350\pi$
$930$	−9.74984			−0.319710
$931$	−0.338181	−	6.07459i	−0.0110834	−	0.199087i
$932$		−	41.9082i		−	1.37275i
$933$	6.26809	+	10.8566i	0.205208	+	0.355431i
$934$	11.9643	−	20.7228i	0.391484	−	0.678071i
$935$	−40.9288	+	67.7565i	−1.33852	+	2.21587i
$936$	−0.275308	+	0.158949i	−0.00899874	+	0.00519542i
$937$	46.7125			1.52603			0.763015	−	0.646380i	$-0.223718\pi$
$937$	46.7125			1.52603			0.763015	+	0.646380i	$0.223718\pi$
$938$	−20.6182	−	4.91452i	−0.673207	−	0.160465i
$939$	−9.56160			−0.312031
$940$	−23.3395	−	40.4252i	−0.761250	−	1.31852i
$941$	−2.66449	+	4.61502i	−0.0868597	+	0.150445i	−0.906182	−	0.422888i	$-0.861017\pi$
$941$	−2.66449	+	4.61502i	−0.0868597	+	0.150445i	0.819322	+	0.573333i	$0.194350\pi$
$942$	−5.52592	−	3.19039i	−0.180044	−	0.103949i
$943$	−5.69179	−	9.85847i	−0.185350	−	0.321036i
$944$			2.89365i			0.0941803i
$945$	−8.33148	+	2.48265i	−0.271023	+	0.0807606i
$946$	−0.390668	+	19.7292i	−0.0127017	+	0.641451i
$947$	−15.3563	−	26.5979i	−0.499012	−	0.864315i	0.500987	−	0.865455i	$-0.332970\pi$
$947$	−15.3563	−	26.5979i	−0.499012	−	0.864315i	−0.999999	+	0.00113997i	$0.999637\pi$
$948$	−5.71737	+	9.90278i	−0.185692	+	0.321627i
$949$	−0.391402	+	0.677929i	−0.0127055	+	0.0220065i
$950$	2.68557	−	1.55051i	0.0871314	−	0.0503053i
$951$			13.8291i			0.448439i
$952$	−29.4342	+	31.1184i	−0.953966	+	1.00855i
$953$		−	13.1207i		−	0.425021i	−0.977159	−	0.212510i	$-0.931836\pi$
$953$		−	13.1207i		−	0.425021i	0.977159	−	0.212510i	$-0.0681640\pi$
$954$	3.53162	−	2.03898i	0.114340	−	0.0660144i
$955$	25.5298	+	14.7396i	0.826125	+	0.476963i
$956$	−10.5178	−	6.07248i	−0.340171	−	0.196398i
$957$	10.7653	−	5.93436i	0.347994	−	0.191831i
$958$		−	9.94604i		−	0.321342i
$959$	−28.2138	−	26.6868i	−0.911071	−	0.861761i
$960$	0.948060			0.0305985
$961$	−3.87995	−	6.72026i	−0.125160	−	0.216783i
$962$	−0.714107	−	0.412290i	−0.0230237	−	0.0132928i
$963$	1.83718	+	1.06069i	0.0592022	+	0.0341804i
$964$	−14.7178	−	25.4919i	−0.474027	−	0.821039i
$965$	−6.93966			−0.223396
$966$	−5.56077	+	1.65702i	−0.178915	+	0.0533138i
$967$			25.7216i			0.827150i	0.910470	+	0.413575i	$0.135720\pi$
$967$			25.7216i			0.827150i	−0.910470	+	0.413575i	$0.864280\pi$
$968$	−21.7012	+	11.4085i	−0.697504	+	0.366682i
$969$	5.46737	+	3.15659i	0.175637	+	0.101404i
$970$	14.1379	+	8.16255i	0.453942	+	0.262084i
$971$	−12.5500	+	7.24576i	−0.402750	+	0.232528i	−0.687670	−	0.726024i	$-0.741366\pi$
$971$	−12.5500	+	7.24576i	−0.402750	+	0.232528i	0.284920	+	0.958551i	$0.408033\pi$
$972$		−	1.62115i		−	0.0519985i
$973$	−2.73313	+	11.4665i	−0.0876202	+	0.367598i
$974$		−	0.0290688i		−	0.000931425i
$975$	0.716016	−	0.413392i	0.0229309	−	0.0132391i
$976$	14.2648	−	24.7073i	0.456605	−	0.790863i
$977$	23.0204	−	39.8725i	0.736488	−	1.27563i	−0.217579	−	0.976043i	$-0.569816\pi$
$977$	23.0204	−	39.8725i	0.736488	−	1.27563i	0.954067	−	0.299592i	$-0.0968506\pi$
$978$	1.91496	+	3.31680i	0.0612336	+	0.106060i
$979$	−26.1254	−	0.517321i	−0.834970	−	0.0165337i
$980$	16.8201	−	33.2787i	0.537300	−	1.06305i
$981$		−	3.22456i		−	0.102952i
$982$	−9.29581	−	16.1008i	−0.296641	−	0.513798i
$983$	−6.26004	−	3.61424i	−0.199664	−	0.115276i	0.396835	−	0.917890i	$-0.370109\pi$
$983$	−6.26004	−	3.61424i	−0.199664	−	0.115276i	−0.596499	+	0.802614i	$0.703442\pi$
$984$	3.56043	−	6.16684i	0.113502	−	0.196592i
$985$	−15.5732	−	26.9735i	−0.496202	−	0.859448i
$986$	16.5706			0.527716
$987$	5.37566	−	22.5528i	0.171109	−	0.717865i
$988$	−0.200967			−0.00639360
$989$	29.8279	−	17.2211i	0.948471	−	0.547600i
$990$	−5.74152	−	3.46821i	−0.182477	−	0.110227i
$991$	9.10070	−	15.7629i	0.289093	−	0.500724i	−0.684500	−	0.729013i	$-0.739980\pi$
$991$	9.10070	−	15.7629i	0.289093	−	0.500724i	0.973594	+	0.228288i	$0.0733129\pi$
$992$	13.5198	+	23.4170i	0.429254	+	0.743491i
$993$			18.2492i			0.579120i
$994$	1.23951	+	4.15966i	0.0393150	+	0.131936i
$995$	4.37880			0.138817
$996$	−8.85943	+	5.11499i	−0.280722	+	0.162075i
$997$	−0.719293	+	1.24585i	−0.0227802	+	0.0394565i	−0.877191	−	0.480142i	$-0.840585\pi$
$997$	−0.719293	+	1.24585i	−0.0227802	+	0.0394565i	0.854411	+	0.519599i	$0.173918\pi$
$998$	−0.804544	−	0.464504i	−0.0254674	−	0.0147036i
$999$	8.13432	−	4.69635i	0.257359	−	0.148586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.p.a.10.10	yes	32
3.2	odd	2		693.2.bg.b.10.7		32
7.3	odd	6		1617.2.c.a.538.20		32
7.4	even	3		1617.2.c.a.538.19		32
7.5	odd	6	inner	231.2.p.a.208.7	yes	32
11.10	odd	2	inner	231.2.p.a.10.7	✓	32
21.5	even	6		693.2.bg.b.208.10		32
33.32	even	2		693.2.bg.b.10.10		32
77.10	even	6		1617.2.c.a.538.14		32
77.32	odd	6		1617.2.c.a.538.13		32
77.54	even	6	inner	231.2.p.a.208.10	yes	32
231.131	odd	6		693.2.bg.b.208.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.7	✓	32	11.10	odd	2	inner
231.2.p.a.10.10	yes	32	1.1	even	1	trivial
231.2.p.a.208.7	yes	32	7.5	odd	6	inner
231.2.p.a.208.10	yes	32	77.54	even	6	inner
693.2.bg.b.10.7		32	3.2	odd	2
693.2.bg.b.10.10		32	33.32	even	2
693.2.bg.b.208.7		32	231.131	odd	6
693.2.bg.b.208.10		32	21.5	even	6
1617.2.c.a.538.13		32	77.32	odd	6
1617.2.c.a.538.14		32	77.10	even	6
1617.2.c.a.538.19		32	7.4	even	3
1617.2.c.a.538.20		32	7.3	odd	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.533044 - 0.307753i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.810576 + 1.40396i) q^{4} +(2.84562 - 1.64292i) q^{5} +0.615506 q^{6} +(-0.613452 + 2.57365i) q^{7} +2.22884i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.533044 - 0.307753i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.810576 + 1.40396i) q^{4} +(2.84562 - 1.64292i) q^{5} +0.615506 q^{6} +(-0.613452 + 2.57365i) q^{7} +2.22884i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.01123 - 1.75150i) q^{10} +(-2.83889 - 1.71485i) q^{11} +(-1.40396 + 0.810576i) q^{12} +0.142630 q^{13} +(0.465052 + 1.56066i) q^{14} +3.28584 q^{15} +(-0.935219 - 1.61985i) q^{16} +(3.63184 - 6.29053i) q^{17} +(0.533044 + 0.307753i) q^{18} +(0.434571 + 0.752699i) q^{19} +5.32684i q^{20} +(-1.81809 + 1.92212i) q^{21} +(-2.04100 - 0.0404149i) q^{22} +(1.78154 + 3.08572i) q^{23} +(-1.11442 + 1.93023i) q^{24} +(2.89836 - 5.02011i) q^{25} +(0.0760278 - 0.0438947i) q^{26} +1.00000i q^{27} +(-3.11605 - 2.94740i) q^{28} +3.70637i q^{29} +(1.75150 - 1.01123i) q^{30} +(-4.17493 - 2.41040i) q^{31} +(-4.85749 - 2.80448i) q^{32} +(-1.60112 - 2.90455i) q^{33} -4.47084i q^{34} +(2.48265 + 8.33148i) q^{35} -1.62115 q^{36} +(-4.69635 - 8.13432i) q^{37} +(0.463291 + 0.267481i) q^{38} +(0.123521 + 0.0713148i) q^{39} +(3.66181 + 6.34243i) q^{40} -3.19487 q^{41} +(-0.377583 + 1.58410i) q^{42} -9.66641i q^{43} +(4.70872 - 2.59566i) q^{44} +(2.84562 + 1.64292i) q^{45} +(1.89928 + 1.09655i) q^{46} +(-7.58896 + 4.38149i) q^{47} -1.87044i q^{48} +(-6.24735 - 3.15762i) q^{49} -3.56792i q^{50} +(6.29053 - 3.63184i) q^{51} +(-0.115612 + 0.200246i) q^{52} +(3.31269 - 5.73774i) q^{53} +(0.307753 + 0.533044i) q^{54} +(-10.8958 - 0.215752i) q^{55} +(-5.73626 - 1.36729i) q^{56} +0.869142i q^{57} +(1.14065 + 1.97566i) q^{58} +(-1.33978 - 0.773522i) q^{59} +(-2.66342 + 4.61318i) q^{60} +(7.62645 + 13.2094i) q^{61} -2.96723 q^{62} +(-2.53557 + 0.755561i) q^{63} +0.288529 q^{64} +(0.405869 - 0.234329i) q^{65} +(-1.74735 - 1.05550i) q^{66} +(-6.50785 + 11.2719i) q^{67} +(5.88777 + 10.1979i) q^{68} +3.56308i q^{69} +(3.88740 + 3.67700i) q^{70} +2.66532 q^{71} +(-1.93023 + 1.11442i) q^{72} +(-2.74419 + 4.75307i) q^{73} +(-5.00673 - 2.89064i) q^{74} +(5.02011 - 2.89836i) q^{75} -1.40901 q^{76} +(6.15495 - 6.25433i) q^{77} +0.0877894 q^{78} +(6.10848 - 3.52673i) q^{79} +(-5.32255 - 3.07298i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.70300 + 0.983230i) q^{82} +6.31032 q^{83} +(-1.22488 - 4.11055i) q^{84} -23.8673i q^{85} +(-2.97487 - 5.15263i) q^{86} +(-1.85319 + 3.20981i) q^{87} +(3.82213 - 6.32743i) q^{88} +(6.82310 - 3.93932i) q^{89} +2.02245 q^{90} +(-0.0874963 + 0.367079i) q^{91} -5.77630 q^{92} +(-2.41040 - 4.17493i) q^{93} +(-2.69683 + 4.67105i) q^{94} +(2.47325 + 1.42793i) q^{95} +(-2.80448 - 4.85749i) q^{96} +8.07193i q^{97} +(-4.30188 + 0.239492i) q^{98} +(0.0656613 - 3.31597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

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