LMFDB - Embedded newform 429.2.t.a.329.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(296,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.296");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.t (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.19
Character	$\chi$	$=$	429.329
Dual form			429.2.t.a.296.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.716153 - 0.413471i) q^{2} +(-1.68064 - 0.418881i) q^{3} +(-0.658083 - 1.13983i) q^{4} -3.60945 q^{5} +(1.03040 + 0.994878i) q^{6} +(-1.45351 - 2.51755i) q^{7} +2.74228i q^{8} +(2.64908 + 1.40797i) q^{9} +O(q^{10})$	\(q+(-0.716153 - 0.413471i) q^{2} +(-1.68064 - 0.418881i) q^{3} +(-0.658083 - 1.13983i) q^{4} -3.60945 q^{5} +(1.03040 + 0.994878i) q^{6} +(-1.45351 - 2.51755i) q^{7} +2.74228i q^{8} +(2.64908 + 1.40797i) q^{9} +(2.58492 + 1.49241i) q^{10} +(-2.69945 - 1.92691i) q^{11} +(0.628544 + 2.19131i) q^{12} +(-2.11573 - 2.91953i) q^{13} +2.40394i q^{14} +(6.06618 + 1.51193i) q^{15} +(-0.182314 + 0.315778i) q^{16} +(-0.309839 - 0.536657i) q^{17} +(-1.31499 - 2.10364i) q^{18} +(1.18049 + 2.04467i) q^{19} +(2.37532 + 4.11418i) q^{20} +(1.38826 + 4.83994i) q^{21} +(1.13650 + 2.49610i) q^{22} +(5.10705 + 2.94856i) q^{23} +(1.14869 - 4.60877i) q^{24} +8.02816 q^{25} +(0.308046 + 2.96563i) q^{26} +(-3.86236 - 3.47594i) q^{27} +(-1.91306 + 3.31352i) q^{28} +(3.36278 - 5.82450i) q^{29} +(-3.71917 - 3.59097i) q^{30} +5.67006i q^{31} +(5.01089 - 2.89304i) q^{32} +(3.72965 + 4.36918i) q^{33} +0.512438i q^{34} +(5.24637 + 9.08699i) q^{35} +(-0.138456 - 3.94607i) q^{36} +(0.225314 + 0.130085i) q^{37} -1.95239i q^{38} +(2.33284 + 5.79291i) q^{39} -9.89813i q^{40} +(-2.92623 - 1.68946i) q^{41} +(1.00696 - 4.04014i) q^{42} +(-8.07839 + 4.66406i) q^{43} +(-0.419892 + 4.34499i) q^{44} +(-9.56172 - 5.08202i) q^{45} +(-2.43829 - 4.22324i) q^{46} -6.20944 q^{47} +(0.438677 - 0.454339i) q^{48} +(-0.725377 + 1.25639i) q^{49} +(-5.74939 - 3.31941i) q^{50} +(0.295931 + 1.03171i) q^{51} +(-1.93545 + 4.33288i) q^{52} +0.712815i q^{53} +(1.32884 + 4.08628i) q^{54} +(9.74354 + 6.95509i) q^{55} +(6.90383 - 3.98593i) q^{56} +(-1.12750 - 3.93083i) q^{57} +(-4.81652 + 2.78082i) q^{58} +(-0.121513 - 0.210467i) q^{59} +(-2.26870 - 7.90942i) q^{60} +(8.04868 - 4.64691i) q^{61} +(2.34440 - 4.06063i) q^{62} +(-0.305808 - 8.71569i) q^{63} -4.05550 q^{64} +(7.63664 + 10.5379i) q^{65} +(-0.864468 - 4.67110i) q^{66} +(-4.43422 - 2.56010i) q^{67} +(-0.407800 + 0.706330i) q^{68} +(-7.34800 - 7.09470i) q^{69} -8.67690i q^{70} +(7.67720 + 13.2973i) q^{71} +(-3.86106 + 7.26450i) q^{72} -13.2442 q^{73} +(-0.107573 - 0.186322i) q^{74} +(-13.4924 - 3.36285i) q^{75} +(1.55372 - 2.69112i) q^{76} +(-0.927415 + 9.59678i) q^{77} +(0.724533 - 5.11317i) q^{78} -0.316398i q^{79} +(0.658055 - 1.13979i) q^{80} +(5.03521 + 7.45967i) q^{81} +(1.39709 + 2.41982i) q^{82} -15.6297i q^{83} +(4.60313 - 4.76747i) q^{84} +(1.11835 + 1.93704i) q^{85} +7.71382 q^{86} +(-8.09138 + 8.38026i) q^{87} +(5.28412 - 7.40264i) q^{88} +(-5.29627 + 9.17341i) q^{89} +(4.74639 + 7.59300i) q^{90} +(-4.27484 + 9.57003i) q^{91} -7.76159i q^{92} +(2.37508 - 9.52930i) q^{93} +(4.44691 + 2.56742i) q^{94} +(-4.26092 - 7.38013i) q^{95} +(-9.63333 + 2.76318i) q^{96} +(12.7818 - 7.37955i) q^{97} +(1.03896 - 0.599844i) q^{98} +(-4.43801 - 8.90528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9}+O(q^{10}) $ 104 * q - 2 * q^3 + 44 * q^4 - 6 * q^9	$ 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9} - 4 q^{12} - 36 q^{15} - 44 q^{16} - 12 q^{22} + 64 q^{25} + 4 q^{27} + 12 q^{33} + 28 q^{36} - 12 q^{37} + 50 q^{42} - 66 q^{45} + 16 q^{48} - 24 q^{49} - 8 q^{55} - 24 q^{58} - 104 q^{64} - 60 q^{66} - 60 q^{67} - 42 q^{69} - 42 q^{75} + 16 q^{78} - 22 q^{81} - 16 q^{82} + 92 q^{88} - 84 q^{91} + 126 q^{93} + 36 q^{97}+O(q^{100}) $ 104 * q - 2 * q^3 + 44 * q^4 - 6 * q^9 - 4 * q^12 - 36 * q^15 - 44 * q^16 - 12 * q^22 + 64 * q^25 + 4 * q^27 + 12 * q^33 + 28 * q^36 - 12 * q^37 + 50 * q^42 - 66 * q^45 + 16 * q^48 - 24 * q^49 - 8 * q^55 - 24 * q^58 - 104 * q^64 - 60 * q^66 - 60 * q^67 - 42 * q^69 - 42 * q^75 + 16 * q^78 - 22 * q^81 - 16 * q^82 + 92 * q^88 - 84 * q^91 + 126 * q^93 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.716153	−	0.413471i	−0.506397	−	0.292368i	0.224955	−	0.974369i	$-0.427777\pi$
$2$	−0.716153	−	0.413471i	−0.506397	−	0.292368i	−0.731351	+	0.682001i	$0.761110\pi$
$3$	−1.68064	−	0.418881i	−0.970316	−	0.241841i
$3$	−1.68064	−	0.418881i	−0.970316	−	0.241841i
$4$	−0.658083	−	1.13983i	−0.329042	−	0.569917i
$5$	−3.60945			−1.61420			−0.807099	−	0.590417i	$-0.798963\pi$
$5$	−3.60945			−1.61420			−0.807099	+	0.590417i	$0.798963\pi$
$6$	1.03040	+	0.994878i	0.420658	+	0.406157i
$7$	−1.45351	−	2.51755i	−0.549375	−	0.951545i	−0.998317	−	0.0579844i	$-0.981533\pi$
$7$	−1.45351	−	2.51755i	−0.549375	−	0.951545i	0.448943	−	0.893561i	$-0.351801\pi$
$8$			2.74228i			0.969542i
$9$	2.64908	+	1.40797i	0.883026	+	0.469325i
$10$	2.58492	+	1.49241i	0.817424	+	0.471940i
$11$	−2.69945	−	1.92691i	−0.813915	−	0.580984i
$11$	−2.69945	−	1.92691i	−0.813915	−	0.580984i
$12$	0.628544	+	2.19131i	0.181445	+	0.632575i
$13$	−2.11573	−	2.91953i	−0.586799	−	0.809733i
$13$	−2.11573	−	2.91953i	−0.586799	−	0.809733i
$14$			2.40394i			0.642479i
$15$	6.06618	+	1.51193i	1.56628	+	0.390380i
$16$	−0.182314	+	0.315778i	−0.0455786	+	0.0789444i
$17$	−0.309839	−	0.536657i	−0.0751470	−	0.130158i	0.826003	−	0.563665i	$-0.190609\pi$
$17$	−0.309839	−	0.536657i	−0.0751470	−	0.130158i	−0.901150	+	0.433507i	$0.857276\pi$
$18$	−1.31499	−	2.10364i	−0.309945	−	0.495833i
$19$	1.18049	+	2.04467i	0.270823	+	0.469079i	0.969073	−	0.246775i	$-0.0793710\pi$
$19$	1.18049	+	2.04467i	0.270823	+	0.469079i	−0.698250	+	0.715854i	$0.746038\pi$
$20$	2.37532	+	4.11418i	0.531138	+	0.919958i
$21$	1.38826	+	4.83994i	0.302944	+	1.05616i
$22$	1.13650	+	2.49610i	0.242302	+	0.532171i
$23$	5.10705	+	2.94856i	1.06489	+	0.614817i	0.926782	−	0.375600i	$-0.122563\pi$
$23$	5.10705	+	2.94856i	1.06489	+	0.614817i	0.138112	+	0.990417i	$0.455897\pi$
$24$	1.14869	−	4.60877i	0.234475	−	0.940762i
$25$	8.02816			1.60563
$26$	0.308046	+	2.96563i	0.0604127	+	0.581607i
$27$	−3.86236	−	3.47594i	−0.743312	−	0.668945i
$28$	−1.91306	+	3.31352i	−0.361534	+	0.626196i
$29$	3.36278	−	5.82450i	0.624452	−	1.08158i	−0.364195	−	0.931323i	$-0.618656\pi$
$29$	3.36278	−	5.82450i	0.624452	−	1.08158i	0.988647	−	0.150259i	$-0.0480109\pi$
$30$	−3.71917	−	3.59097i	−0.679025	−	0.655618i
$31$			5.67006i			1.01837i	0.860656	+	0.509186i	$0.170054\pi$
$31$			5.67006i			1.01837i	−0.860656	+	0.509186i	$0.829946\pi$
$32$	5.01089	−	2.89304i	0.885809	−	0.511422i
$33$	3.72965	+	4.36918i	0.649248	+	0.760577i
$34$			0.512438i			0.0878824i
$35$	5.24637	+	9.08699i	0.886799	+	1.53598i
$36$	−0.138456	−	3.94607i	−0.0230760	−	0.657679i
$37$	0.225314	+	0.130085i	0.0370414	+	0.0213859i	0.518406	−	0.855134i	$-0.326525\pi$
$37$	0.225314	+	0.130085i	0.0370414	+	0.0213859i	−0.481365	+	0.876520i	$0.659859\pi$
$38$		−	1.95239i		−	0.316720i
$39$	2.33284	+	5.79291i	0.373553	+	0.927609i
$40$		−	9.89813i		−	1.56503i
$41$	−2.92623	−	1.68946i	−0.457000	−	0.263849i	0.253782	−	0.967261i	$-0.418325\pi$
$41$	−2.92623	−	1.68946i	−0.457000	−	0.263849i	−0.710782	+	0.703412i	$0.751659\pi$
$42$	1.00696	−	4.04014i	0.155378	−	0.623407i
$43$	−8.07839	+	4.66406i	−1.23194	+	0.711263i	−0.967435	−	0.253121i	$-0.918543\pi$
$43$	−8.07839	+	4.66406i	−1.23194	+	0.711263i	−0.264508	+	0.964383i	$0.585210\pi$
$44$	−0.419892	+	4.34499i	−0.0633011	+	0.655032i
$45$	−9.56172	−	5.08202i	−1.42538	−	0.757583i
$46$	−2.43829	−	4.22324i	−0.359506	−	0.622682i
$47$	−6.20944			−0.905740			−0.452870	−	0.891577i	$-0.649600\pi$
$47$	−6.20944			−0.905740			−0.452870	+	0.891577i	$0.649600\pi$
$48$	0.438677	−	0.454339i	0.0633176	−	0.0655782i
$49$	−0.725377	+	1.25639i	−0.103625	+	0.179484i
$50$	−5.74939	−	3.31941i	−0.813087	−	0.469436i
$51$	0.295931	+	1.03171i	0.0414387	+	0.144468i
$52$	−1.93545	+	4.33288i	−0.268399	+	0.600862i
$53$			0.712815i			0.0979126i	0.998801	+	0.0489563i	$0.0155895\pi$
$53$			0.712815i			0.0979126i	−0.998801	+	0.0489563i	$0.984410\pi$
$54$	1.32884	+	4.08628i	0.180832	+	0.556072i
$55$	9.74354	+	6.95509i	1.31382	+	0.937824i
$56$	6.90383	−	3.98593i	0.922562	−	0.532642i
$57$	−1.12750	−	3.93083i	−0.149341	−	0.520651i
$58$	−4.81652	+	2.78082i	−0.632440	+	0.365140i
$59$	−0.121513	−	0.210467i	−0.0158196	−	0.0274004i	0.858007	−	0.513638i	$-0.171702\pi$
$59$	−0.121513	−	0.210467i	−0.0158196	−	0.0274004i	−0.873827	+	0.486237i	$0.838369\pi$
$60$	−2.26870	−	7.90942i	−0.292888	−	1.02110i
$61$	8.04868	−	4.64691i	1.03053	−	0.594975i	0.113392	−	0.993550i	$-0.463828\pi$
$61$	8.04868	−	4.64691i	1.03053	−	0.594975i	0.917136	+	0.398575i	$0.130495\pi$
$62$	2.34440	−	4.06063i	0.297740	−	0.515700i
$63$	−0.305808	−	8.71569i	−0.0385282	−	1.09807i
$64$	−4.05550			−0.506937
$65$	7.63664	+	10.5379i	0.947209	+	1.30707i
$66$	−0.864468	−	4.67110i	−0.106409	−	0.574973i
$67$	−4.43422	−	2.56010i	−0.541726	−	0.312765i	0.204052	−	0.978960i	$-0.434589\pi$
$67$	−4.43422	−	2.56010i	−0.541726	−	0.312765i	−0.745778	+	0.666194i	$0.767922\pi$
$68$	−0.407800	+	0.706330i	−0.0494530	+	0.0856551i
$69$	−7.34800	−	7.09470i	−0.884596	−	0.854102i
$70$		−	8.67690i		−	1.03709i
$71$	7.67720	+	13.2973i	0.911116	+	1.57810i	0.812491	+	0.582974i	$0.198111\pi$
$71$	7.67720	+	13.2973i	0.911116	+	1.57810i	0.0986246	+	0.995125i	$0.468556\pi$
$72$	−3.86106	+	7.26450i	−0.455030	+	0.856130i
$73$	−13.2442			−1.55011			−0.775057	−	0.631891i	$-0.782279\pi$
$73$	−13.2442			−1.55011			−0.775057	+	0.631891i	$0.782279\pi$
$74$	−0.107573	−	0.186322i	−0.0125051	−	0.0216595i
$75$	−13.4924	−	3.36285i	−1.55797	−	0.388308i
$76$	1.55372	−	2.69112i	0.178224	−	0.308693i
$77$	−0.927415	+	9.59678i	−0.105689	+	1.09365i
$78$	0.724533	−	5.11317i	0.0820372	−	0.578953i
$79$		−	0.316398i		−	0.0355975i	−0.999842	−	0.0177988i	$-0.994334\pi$
$79$		−	0.316398i		−	0.0355975i	0.999842	−	0.0177988i	$-0.00566582\pi$
$80$	0.658055	−	1.13979i	0.0735728	−	0.127432i
$81$	5.03521	+	7.45967i	0.559468	+	0.828852i
$82$	1.39709	+	2.41982i	0.154282	+	0.267225i
$83$		−	15.6297i		−	1.71558i	−0.513997	−	0.857792i	$-0.671836\pi$
$83$		−	15.6297i		−	1.71558i	0.513997	−	0.857792i	$-0.328164\pi$
$84$	4.60313	−	4.76747i	0.502243	−	0.520174i
$85$	1.11835	+	1.93704i	0.121302	+	0.210101i
$86$	7.71382			0.831802
$87$	−8.09138	+	8.38026i	−0.867487	+	0.898458i
$88$	5.28412	−	7.40264i	0.563289	−	0.789124i
$89$	−5.29627	+	9.17341i	−0.561403	+	0.972379i	0.435971	+	0.899961i	$0.356405\pi$
$89$	−5.29627	+	9.17341i	−0.561403	+	0.972379i	−0.997374	+	0.0724184i	$0.976928\pi$
$90$	4.74639	+	7.59300i	0.500313	+	0.800372i
$91$	−4.27484	+	9.57003i	−0.448125	+	1.00321i
$92$		−	7.76159i		−	0.809202i
$93$	2.37508	−	9.52930i	0.246284	−	0.988143i
$94$	4.44691	+	2.56742i	0.458664	+	0.264810i
$95$	−4.26092	−	7.38013i	−0.437161	−	0.757186i
$96$	−9.63333	+	2.76318i	−0.983198	+	0.282016i
$97$	12.7818	−	7.37955i	1.29779	−	0.749279i	0.317768	−	0.948168i	$-0.397067\pi$
$97$	12.7818	−	7.37955i	1.29779	−	0.749279i	0.980022	+	0.198889i	$0.0637333\pi$
$98$	1.03896	−	0.599844i	0.104951	−	0.0605934i
$99$	−4.43801	−	8.90528i	−0.446037	−	0.895015i
$100$	−5.28320	−	9.15077i	−0.528320	−	0.915077i
$101$	−7.75309	+	13.4287i	−0.771461	+	1.33621i	0.165301	+	0.986243i	$0.447140\pi$
$101$	−7.75309	+	13.4287i	−0.771461	+	1.33621i	−0.936762	+	0.349967i	$0.886193\pi$
$102$	0.214651	−	0.861222i	0.0212536	−	0.0852737i
$103$	−18.8109			−1.85349			−0.926747	−	0.375686i	$-0.877407\pi$
$103$	−18.8109			−1.85349			−0.926747	+	0.375686i	$0.877407\pi$
$104$	8.00617	−	5.80193i	0.785070	−	0.568926i
$105$	−5.01088	−	17.4695i	−0.489012	−	1.70485i
$106$	0.294728	−	0.510484i	0.0286265	−	0.0495826i
$107$	−4.77385	+	8.26856i	−0.461506	+	0.799352i	−0.999036	−	0.0438927i	$-0.986024\pi$
$107$	−4.77385	+	8.26856i	−0.461506	+	0.799352i	0.537530	+	0.843244i	$0.319357\pi$
$108$	−1.42024	+	6.68991i	−0.136663	+	0.643737i
$109$	6.66701			0.638584			0.319292	−	0.947656i	$-0.396555\pi$
$109$	6.66701			0.638584			0.319292	+	0.947656i	$0.396555\pi$
$110$	−4.10214	−	9.00958i	−0.391123	−	0.859029i
$111$	−0.324181	−	0.313006i	−0.0307699	−	0.0297092i
$112$	1.05998			0.100159
$113$	8.81795	−	5.09105i	0.829523	−	0.478926i	−0.0241661	−	0.999708i	$-0.507693\pi$
$113$	8.81795	−	5.09105i	0.829523	−	0.478926i	0.853689	+	0.520782i	$0.174360\pi$
$114$	−0.817821	+	3.28126i	−0.0765959	+	0.307318i
$115$	−18.4337	−	10.6427i	−1.71895	−	0.992436i
$116$	−8.85195			−0.821883
$117$	−1.49411	−	10.7130i	−0.138130	−	0.990414i
$118$			0.200968i			0.0185006i
$119$	−0.900708	+	1.56007i	−0.0825678	+	0.143012i
$120$	−4.14614	+	16.6352i	−0.378489	+	1.51857i
$121$	3.57405	+	10.4032i	0.324914	+	0.945744i
$122$	−7.68544			−0.695807
$123$	4.21024	+	4.06511i	0.379625	+	0.366539i
$124$	6.46292	−	3.73137i	0.580388	−	0.335087i
$125$	−10.9300			−0.977611
$126$	−3.38468	+	6.36821i	−0.301531	+	0.567325i
$127$	11.2624	+	6.50233i	0.999373	+	0.576988i	0.908063	−	0.418834i	$-0.137561\pi$
$127$	11.2624	+	6.50233i	0.999373	+	0.576988i	0.0913103	+	0.995822i	$0.470894\pi$
$128$	−7.11743	−	4.10925i	−0.629098	−	0.363210i
$129$	15.5305	−	4.45470i	1.36739	−	0.392215i
$130$	−1.11188	−	10.7043i	−0.0975180	−	0.938829i
$131$	−1.19424			−0.104341			−0.0521706	−	0.998638i	$-0.516614\pi$
$131$	−1.19424			−0.104341			−0.0521706	+	0.998638i	$0.516614\pi$
$132$	2.52572	−	7.12646i	0.219836	−	0.620279i
$133$	3.43170	−	5.94388i	0.297566	−	0.515400i
$134$	2.11705	+	3.66684i	0.182885	+	0.316767i
$135$	13.9410	+	12.5463i	1.19985	+	1.07981i
$136$	1.47166	−	0.849665i	0.126194	−	0.0728582i
$137$	0.795650	+	1.37811i	0.0679769	+	0.117740i	0.898011	−	0.439974i	$-0.145012\pi$
$137$	0.795650	+	1.37811i	0.0679769	+	0.117740i	−0.830034	+	0.557713i	$0.811679\pi$
$138$	2.32884	+	8.11908i	0.198244	+	0.691142i
$139$	6.24093	−	3.60320i	0.529349	−	0.305620i	−0.211402	−	0.977399i	$-0.567803\pi$
$139$	6.24093	−	3.60320i	0.529349	−	0.305620i	0.740751	+	0.671779i	$0.234470\pi$
$140$	6.90510	−	11.9600i	0.583588	−	1.01080i
$141$	10.4358	+	2.60102i	0.878854	+	0.219045i
$142$		−	12.6972i		−	1.06552i
$143$	0.0856427	+	11.9580i	0.00716180	+	0.999974i
$144$	−0.927571	+	0.579825i	−0.0772976	+	0.0483188i
$145$	−12.1378	+	21.0233i	−1.00799	+	1.74589i
$146$	9.48486	+	5.47609i	0.784972	+	0.453204i
$147$	1.74537	−	1.80769i	0.143956	−	0.149095i
$148$		−	0.342428i		−	0.0281474i
$149$	−0.645717	+	0.372805i	−0.0528992	+	0.0305414i	−0.526216	−	0.850351i	$-0.676390\pi$
$149$	−0.645717	+	0.372805i	−0.0528992	+	0.0305414i	0.473317	+	0.880892i	$0.343056\pi$
$150$	8.27220	+	7.98704i	0.675422	+	0.652139i
$151$	−5.46182			−0.444477			−0.222238	−	0.974992i	$-0.571336\pi$
$151$	−5.46182			−0.444477			−0.222238	+	0.974992i	$0.571336\pi$
$152$	−5.60704	+	3.23723i	−0.454791	+	0.262574i
$153$	−0.0651880	−	1.85789i	−0.00527014	−	0.150202i
$154$	4.63216	−	6.48930i	0.373270	−	0.522923i
$155$		−	20.4658i		−	1.64385i
$156$	5.06776	−	6.47127i	0.405745	−	0.518116i
$157$	8.52908			0.680695			0.340347	−	0.940300i	$-0.389455\pi$
$157$	8.52908			0.680695			0.340347	+	0.940300i	$0.389455\pi$
$158$	−0.130821	+	0.226589i	−0.0104076	+	0.0180265i
$159$	0.298585	−	1.19798i	0.0236793	−	0.0950062i
$160$	−18.0866	+	10.4423i	−1.42987	+	0.825536i
$161$		−	17.1430i		−	1.35106i
$162$	−0.521628	−	7.42418i	−0.0409829	−	0.583298i
$163$	−11.4306	+	6.59946i	−0.895314	+	0.516910i	−0.875677	−	0.482897i	$-0.839584\pi$
$163$	−11.4306	+	6.59946i	−0.895314	+	0.516910i	−0.0196371	+	0.999807i	$0.506251\pi$
$164$			4.44722i			0.347270i
$165$	−13.4620	−	15.7704i	−1.04801	−	1.22772i
$166$	−6.46243	+	11.1933i	−0.501582	+	0.868766i
$167$	18.4673	+	10.6621i	1.42904	+	0.825057i	0.997045	−	0.0768186i	$-0.0244762\pi$
$167$	18.4673	+	10.6621i	1.42904	+	0.825057i	0.431996	+	0.901876i	$0.357810\pi$
$168$	−13.2724	+	3.80701i	−1.02399	+	0.293717i
$169$	−4.04735	+	12.3539i	−0.311335	+	0.950300i
$170$		−	1.84962i		−	0.141860i
$171$	0.248367	+	7.07858i	0.0189931	+	0.541312i
$172$	10.6325	+	6.13868i	0.810721	+	0.468070i
$173$	5.03566	+	8.72202i	0.382854	+	0.663123i	0.991469	−	0.130343i	$-0.0416078\pi$
$173$	5.03566	+	8.72202i	0.382854	+	0.663123i	−0.608615	+	0.793466i	$0.708275\pi$
$174$	9.25966	−	2.65600i	0.701973	−	0.201351i
$175$	−11.6690	−	20.2113i	−0.882094	−	1.52783i
$176$	1.10062	−	0.501123i	0.0829625	−	0.0377736i
$177$	0.116059	+	0.404618i	0.00872350	+	0.0304129i
$178$	7.58588	−	4.37971i	0.568585	−	0.328273i
$179$	−9.04701	−	5.22330i	−0.676205	−	0.390407i	0.122218	−	0.992503i	$-0.460999\pi$
$179$	−9.04701	−	5.22330i	−0.676205	−	0.390407i	−0.798424	+	0.602096i	$0.794333\pi$
$180$	0.499751	+	14.2432i	0.0372493	+	1.06162i
$181$	17.7170			1.31690			0.658448	−	0.752626i	$-0.271213\pi$
$181$	17.7170			1.31690			0.658448	+	0.752626i	$0.271213\pi$
$182$	7.01837	−	5.08608i	0.520236	−	0.377006i
$183$	−15.4734	+	4.43832i	−1.14383	+	0.328090i
$184$	−8.08577	+	14.0050i	−0.596091	+	1.03246i
$185$	−0.813261	−	0.469537i	−0.0597922	−	0.0345210i
$186$	−5.64101	+	5.84241i	−0.413619	+	0.428386i
$187$	−0.197694	+	2.04571i	−0.0144568	+	0.149597i
$188$	4.08633	+	7.07773i	0.298026	+	0.516197i
$189$	−3.13689	+	14.7760i	−0.228175	+	1.07480i
$190$			7.04707i			0.511248i
$191$	3.82809	−	2.21015i	0.276991	−	0.159921i	−0.355070	−	0.934840i	$-0.615543\pi$
$191$	3.82809	−	2.21015i	0.276991	−	0.159921i	0.632060	+	0.774919i	$0.282209\pi$
$192$	6.81582	+	1.69877i	0.491889	+	0.122598i
$193$	−0.123929	+	0.214651i	−0.00892061	+	0.0154509i	−0.870451	−	0.492255i	$-0.836173\pi$
$193$	−0.123929	+	0.214651i	−0.00892061	+	0.0154509i	0.861531	+	0.507706i	$0.169506\pi$
$194$	−12.2049			−0.876262
$195$	−8.42028	−	20.9093i	−0.602989	−	1.49734i
$196$	1.90943			0.136388
$197$	−3.20326	−	1.84940i	−0.228223	−	0.131765i	0.381529	−	0.924357i	$-0.375398\pi$
$197$	−3.20326	−	1.84940i	−0.228223	−	0.131765i	−0.609752	+	0.792592i	$0.708731\pi$
$198$	−0.503782	+	8.21253i	−0.0358022	+	0.583639i
$199$	2.15254	+	3.72831i	0.152590	+	0.264293i	0.932179	−	0.361998i	$-0.117905\pi$
$199$	2.15254	+	3.72831i	0.152590	+	0.264293i	−0.779589	+	0.626291i	$0.784572\pi$
$200$			22.0155i			1.55673i
$201$	6.37993	+	6.16000i	0.450005	+	0.434493i
$202$	11.1048	−	6.41136i	0.781331	−	0.451101i
$203$	−19.5513			−1.37223
$204$	0.981232	−	1.01626i	0.0687000	−	0.0711528i
$205$	10.5621	+	6.09803i	0.737689	+	0.425905i
$206$	13.4715	+	7.77777i	0.938603	+	0.541903i
$207$	9.37748	+	15.0016i	0.651780	+	1.04268i
$208$	1.30765	−	0.135828i	0.0906693	−	0.00941800i
$209$	0.753214	−	7.79417i	0.0521009	−	0.539134i
$210$	−3.63459	+	14.5827i	−0.250811	+	1.00630i
$211$	11.2825	+	6.51393i	0.776716	+	0.448437i	0.835265	−	0.549847i	$-0.185314\pi$
$211$	11.2825	+	6.51393i	0.776716	+	0.448437i	−0.0585490	+	0.998285i	$0.518647\pi$
$212$	0.812490	−	0.469092i	0.0558021	−	0.0322173i
$213$	−7.33259	−	25.5638i	−0.502420	−	1.75160i
$214$	6.83762	−	3.94770i	0.467410	−	0.269859i
$215$	29.1586	−	16.8347i	1.98860	−	1.14812i
$216$	9.53200	−	10.5917i	0.648570	−	0.720671i
$217$	14.2747	−	8.24148i	0.969027	−	0.559468i
$218$	−4.77460	−	2.75662i	−0.323377	−	0.186702i
$219$	22.2587	+	5.54774i	1.50410	+	0.374882i
$220$	1.51558	−	15.6830i	0.102180	−	1.05735i
$221$	−0.911252	+	2.04001i	−0.0612974	+	0.137226i
$222$	0.102744	+	0.358199i	0.00689574	+	0.0240408i
$223$	−3.59489	−	2.07551i	−0.240732	−	0.138987i	0.374781	−	0.927113i	$-0.377718\pi$
$223$	−3.59489	−	2.07551i	−0.240732	−	0.138987i	−0.615513	+	0.788127i	$0.711051\pi$
$224$	−14.5668	−	8.41012i	−0.973283	−	0.561925i
$225$	21.2672	+	11.3035i	1.41781	+	0.753563i
$226$	−8.42000			−0.560090
$227$	−7.31729	+	4.22464i	−0.485665	+	0.280399i	−0.722774	−	0.691084i	$-0.757133\pi$
$227$	−7.31729	+	4.22464i	−0.485665	+	0.280399i	0.237109	+	0.971483i	$0.423800\pi$
$228$	−3.73850	+	3.87197i	−0.247588	+	0.256428i
$229$			15.9604i			1.05469i	0.849650	+	0.527346i	$0.176813\pi$
$229$			15.9604i			1.05469i	−0.849650	+	0.527346i	$0.823187\pi$
$230$	8.80089	+	15.2436i	0.580313	+	1.00513i
$231$	5.57856	−	15.7402i	0.367042	−	1.03563i
$232$	15.9724	+	9.22167i	1.04864	+	0.605432i
$233$	−14.4909			−0.949331			−0.474666	−	0.880166i	$-0.657431\pi$
$233$	−14.4909			−0.949331			−0.474666	+	0.880166i	$0.657431\pi$
$234$	−3.35949	+	8.28989i	−0.219617	+	0.541927i
$235$	22.4127			1.46204
$236$	−0.159931	+	0.277009i	−0.0104106	+	0.0180318i
$237$	−0.132533	+	0.531749i	−0.00860895	+	0.0345408i
$238$	1.29009	−	0.744833i	0.0836241	−	0.0482804i
$239$		−	0.504548i		−	0.0326365i	−0.999867	−	0.0163182i	$-0.994806\pi$
$239$		−	0.504548i		−	0.0326365i	0.999867	−	0.0163182i	$-0.00519449\pi$
$240$	−1.58339	+	1.63992i	−0.102207	+	0.105856i
$241$	9.18385	+	15.9069i	0.591584	+	1.02465i	0.994019	+	0.109205i	$0.0348305\pi$
$241$	9.18385	+	15.9069i	0.591584	+	1.02465i	−0.402435	+	0.915448i	$0.631836\pi$
$242$	1.74184	−	8.92803i	0.111970	−	0.573916i
$243$	−5.33765	−	14.6461i	−0.342410	−	0.939551i
$244$	−10.5934	−	6.11610i	−0.678173	−	0.391543i
$245$	2.61821	−	4.53488i	0.167272	−	0.289723i
$246$	−1.33437	−	4.65205i	−0.0850765	−	0.296604i
$247$	3.47187	−	7.77244i	0.220910	−	0.494549i
$248$	−15.5489			−0.987354
$249$	−6.54699	+	26.2679i	−0.414899	+	1.66466i
$250$	7.82756	+	4.51925i	0.495059	+	0.285822i
$251$	−10.8243	+	6.24940i	−0.683222	+	0.394459i	−0.801068	−	0.598573i	$-0.795735\pi$
$251$	−10.8243	+	6.24940i	−0.683222	+	0.394459i	0.117846	+	0.993032i	$0.462401\pi$
$252$	−9.73319	+	6.08422i	−0.613133	+	0.383270i
$253$	−8.10463	−	17.8003i	−0.509534	−	1.11910i
$254$	−5.37705	−	9.31332i	−0.337386	−	0.584370i
$255$	−1.06815	−	3.72392i	−0.0668902	−	0.233201i
$256$	7.45361	+	12.9100i	0.465851	+	0.806877i
$257$	−8.57172	−	4.94889i	−0.534689	−	0.308703i	0.208235	−	0.978079i	$-0.433228\pi$
$257$	−8.57172	−	4.94889i	−0.534689	−	0.308703i	−0.742924	+	0.669376i	$0.766562\pi$
$258$	−12.9641	−	3.23117i	−0.807111	−	0.201164i
$259$		−	0.756320i		−	0.0469954i
$260$	6.98594	−	15.6393i	0.433249	−	0.969910i
$261$	17.1090	−	10.6948i	1.05902	−	0.661994i
$262$	0.855258	+	0.493783i	0.0528380	+	0.0305060i
$263$	−5.57568	+	9.65736i	−0.343811	+	0.595498i	−0.985137	−	0.171770i	$-0.945051\pi$
$263$	−5.57568	+	9.65736i	−0.343811	+	0.595498i	0.641326	+	0.767269i	$0.278385\pi$
$264$	−11.9815	+	10.2277i	−0.737411	+	0.629473i
$265$		−	2.57287i		−	0.158050i
$266$	−4.91525	+	2.83782i	−0.301373	+	0.173998i
$267$	12.7437	−	13.1987i	0.779900	−	0.807744i
$268$			6.73903i			0.411652i
$269$	0.197250	−	0.113882i	0.0120266	−	0.00694353i	−0.493975	−	0.869476i	$-0.664456\pi$
$269$	0.197250	−	0.113882i	0.0120266	−	0.00694353i	0.506001	+	0.862533i	$0.331123\pi$
$270$	−4.79638	−	14.7492i	−0.291899	−	0.897610i
$271$	2.56137	−	4.43643i	0.155592	−	0.269494i	−0.777682	−	0.628658i	$-0.783605\pi$
$271$	2.56137	−	4.43643i	0.155592	−	0.269494i	0.933275	+	0.359164i	$0.116938\pi$
$272$	0.225952			0.0137004
$273$	11.1932	−	14.2931i	0.677441	−	0.865057i
$274$		−	1.31591i		−	0.0794972i
$275$	−21.6716	−	15.4695i	−1.30685	−	0.932848i
$276$	−3.25119	+	13.0444i	−0.195698	+	0.785181i
$277$	−0.815907	+	0.471064i	−0.0490231	+	0.0283035i	−0.524311	−	0.851527i	$-0.675677\pi$
$277$	−0.815907	+	0.471064i	−0.0490231	+	0.0283035i	0.475288	+	0.879830i	$0.342344\pi$
$278$	−5.95928			−0.357414
$279$	−7.98330	+	15.0204i	−0.477947	+	0.899249i
$280$	−24.9190	+	14.3870i	−1.48920	+	0.859789i
$281$		−	17.7047i		−	1.05618i	−0.849190	−	0.528088i	$-0.822909\pi$
$281$		−	17.7047i		−	1.05618i	0.849190	−	0.528088i	$-0.177091\pi$
$282$	−6.39819	−	6.17763i	−0.381007	−	0.367873i
$283$	4.13971	+	2.39006i	0.246080	+	0.142075i	0.617968	−	0.786203i	$-0.287956\pi$
$283$	4.13971	+	2.39006i	0.246080	+	0.142075i	−0.371888	+	0.928278i	$0.621289\pi$
$284$	10.1045	−	17.5015i	0.599590	−	1.03852i
$285$	4.06966	+	14.1881i	0.241066	+	0.840433i
$286$	4.88293	−	8.59913i	0.288734	−	0.508477i
$287$			9.82258i			0.579808i
$288$	17.3476	−	0.608676i	1.02222	−	0.0358666i
$289$	8.30800	−	14.3899i	0.488706	−	0.846463i
$290$	17.3850	−	10.0372i	1.02088	−	0.589407i
$291$	−24.5726	+	7.04830i	−1.44047	+	0.413178i
$292$	8.71578	+	15.0962i	0.510052	+	0.883436i
$293$	−14.7021	+	8.48825i	−0.858905	+	0.495889i	−0.863645	−	0.504100i	$-0.831824\pi$
$293$	−14.7021	+	8.48825i	−0.858905	+	0.495889i	0.00474047	+	0.999989i	$0.498491\pi$
$294$	−1.99738	+	0.572919i	−0.116490	+	0.0334133i
$295$	0.438596	+	0.759670i	0.0255360	+	0.0442297i
$296$	−0.356730	+	0.617874i	−0.0207345	+	0.0359132i
$297$	3.72843	+	16.8255i	0.216345	+	0.976317i
$298$	0.616576			0.0357173
$299$	−2.19674	−	21.1486i	−0.127041	−	1.22305i
$300$	5.04605	+	17.5922i	0.291334	+	1.01568i
$301$	23.4840	+	13.5585i	1.35360	+	0.781499i
$302$	3.91150	+	2.25831i	0.225082	+	0.129951i
$303$	18.6552	−	19.3212i	1.07171	−	1.10997i
$304$	−0.860880			−0.0493749
$305$	−29.0513	+	16.7728i	−1.66347	+	0.960408i
$306$	−0.721500	+	1.35749i	−0.0412454	+	0.0776024i
$307$	−26.7631			−1.52745			−0.763725	−	0.645542i	$-0.776632\pi$
$307$	−26.7631			−1.52745			−0.763725	+	0.645542i	$0.776632\pi$
$308$	11.5491	−	5.25838i	0.658068	−	0.299624i
$309$	31.6143	+	7.87954i	1.79847	+	0.448251i
$310$	−8.46202	+	14.6566i	−0.480610	+	0.832442i
$311$			0.437159i			0.0247890i	0.999923	+	0.0123945i	$0.00394539\pi$
$311$			0.437159i			0.0247890i	−0.999923	+	0.0123945i	$0.996055\pi$
$312$	−15.8858	+	6.39729i	−0.899355	+	0.362175i
$313$	−14.0254			−0.792764			−0.396382	−	0.918086i	$-0.629734\pi$
$313$	−14.0254			−0.792764			−0.396382	+	0.918086i	$0.629734\pi$
$314$	−6.10813	−	3.52653i	−0.344701	−	0.199014i
$315$	1.10380	+	31.4589i	0.0621921	+	1.77251i
$316$	−0.360641	+	0.208216i	−0.0202876	+	0.0117131i
$317$	1.32272			0.0742914			0.0371457	−	0.999310i	$-0.488173\pi$
$317$	1.32272			0.0742914			0.0371457	+	0.999310i	$0.488173\pi$
$318$	−0.709163	+	0.734482i	−0.0397679	+	0.0411877i
$319$	−20.3009	+	9.24318i	−1.13663	+	0.517519i
$320$	14.6381			0.818297
$321$	11.4867	−	11.8968i	0.641123	−	0.664012i
$322$	−7.08814	+	12.2770i	−0.395007	+	0.684172i
$323$	0.731523	−	1.26704i	0.0407030	−	0.0704997i
$324$	5.18919	−	10.6484i	0.288288	−	0.591577i
$325$	−16.9854	−	23.4385i	−0.942183	−	1.30013i
$326$	10.9147			0.604512
$327$	−11.2048	−	2.79269i	−0.619628	−	0.154436i
$328$	4.63297	−	8.02453i	0.255813	−	0.443081i
$329$	9.02548	+	15.6326i	0.497591	+	0.861852i
$330$	3.12026	+	16.8601i	0.171765	+	0.928120i
$331$	−19.4419	+	11.2248i	−1.06862	+	0.616971i	−0.927805	−	0.373064i	$-0.878307\pi$
$331$	−19.4419	+	11.2248i	−1.06862	+	0.616971i	−0.140819	+	0.990035i	$0.544974\pi$
$332$	−17.8153	+	10.2857i	−0.977740	+	0.564498i
$333$	0.413718	+	0.661842i	0.0226716	+	0.0362687i
$334$	−8.81693	−	15.2714i	−0.482441	−	0.835612i
$335$	16.0051	+	9.24055i	0.874452	+	0.504865i
$336$	−1.78144	−	0.444007i	−0.0971857	−	0.0242226i
$337$		−	14.1245i		−	0.769412i	−0.923039	−	0.384706i	$-0.874303\pi$
$337$		−	14.1245i		−	0.769412i	0.923039	−	0.384706i	$-0.125697\pi$
$338$	8.00650	−	7.17382i	0.435496	−	0.390204i
$339$	−16.9523	+	4.86252i	−0.920724	+	0.264096i
$340$	1.47194	−	2.54947i	0.0798269	−	0.138264i
$341$	10.9257	−	15.3060i	0.591658	−	0.828868i
$342$	2.74892	−	5.17204i	0.148644	−	0.279672i
$343$	−16.1318			−0.871033
$344$	−12.7902	−	22.1532i	−0.689599	−	1.19442i
$345$	26.5223	+	25.6080i	1.42791	+	1.37869i
$346$		−	8.32840i		−	0.447737i
$347$	11.7907	+	20.4220i	0.632955	+	1.09631i	0.986944	+	0.161061i	$0.0514917\pi$
$347$	11.7907	+	20.4220i	0.632955	+	1.09631i	−0.353989	+	0.935250i	$0.615175\pi$
$348$	14.8769	+	3.70792i	0.797486	+	0.198765i
$349$	−12.2094	+	21.1474i	−0.653556	+	1.13199i	0.328697	+	0.944435i	$0.393390\pi$
$349$	−12.2094	+	21.1474i	−0.653556	+	1.13199i	−0.982254	+	0.187557i	$0.939943\pi$
$350$			19.2992i			1.03158i
$351$	−1.97641	+	18.6305i	−0.105493	+	0.994420i
$352$	−19.1013	−	1.84591i	−1.01810	−	0.0983874i
$353$	4.65200	−	8.05750i	0.247601	−	0.428857i	−0.715259	−	0.698860i	$-0.753691\pi$
$353$	4.65200	−	8.05750i	0.247601	−	0.428857i	0.962860	+	0.270002i	$0.0870245\pi$
$354$	0.0841819	−	0.337755i	0.00447422	−	0.0179515i
$355$	−27.7105	−	47.9960i	−1.47072	−	2.54736i
$356$	13.9415			0.738900
$357$	2.16725	−	2.24462i	0.114703	−	0.118798i
$358$	4.31936	+	7.48136i	0.228285	+	0.395402i
$359$			5.02549i			0.265235i	0.991167	+	0.132618i	$0.0423382\pi$
$359$			5.02549i			0.265235i	−0.991167	+	0.132618i	$0.957662\pi$
$360$	13.9363	−	26.2209i	0.734508	−	1.38196i
$361$	6.71289	−	11.6271i	0.353310	−	0.611951i
$362$	−12.6881	−	7.32548i	−0.666872	−	0.385019i
$363$	−1.64899	−	18.9811i	−0.0865494	−	0.996248i
$364$	13.7214	−	1.42527i	0.719199	−	0.0747047i
$365$	47.8043			2.50219
$366$	12.9164	+	3.21929i	0.675153	+	0.168275i
$367$	−10.9474	+	18.9615i	−0.571451	+	0.989782i	0.424966	+	0.905209i	$0.360286\pi$
$367$	−10.9474	+	18.9615i	−0.571451	+	0.989782i	−0.996417	+	0.0845732i	$0.973047\pi$
$368$	−1.86218	+	1.07513i	−0.0970727	+	0.0560450i
$369$	−5.37309	−	8.59556i	−0.279712	−	0.447467i
$370$	0.388280	+	0.672520i	0.0201857	+	0.0349627i
$371$	1.79455	−	1.03608i	0.0931683	−	0.0537907i
$372$	−12.4248	+	3.56388i	−0.644197	+	0.184778i
$373$	17.6888	−	10.2126i	0.915890	−	0.528789i	0.0335684	−	0.999436i	$-0.489313\pi$
$373$	17.6888	−	10.2126i	0.915890	−	0.528789i	0.882322	+	0.470647i	$0.155979\pi$
$374$	0.987421	−	1.38330i	0.0510583	−	0.0715288i
$375$	18.3694	+	4.57838i	0.948591	+	0.236427i
$376$		−	17.0280i		−	0.878153i
$377$	−24.1196	+	2.50535i	−1.24222	+	0.129032i
$378$	8.35594	−	9.28486i	0.429783	−	0.477562i
$379$	−2.07421	−	1.19754i	−0.106545	−	0.0615137i	0.445781	−	0.895142i	$-0.352926\pi$
$379$	−2.07421	−	1.19754i	−0.106545	−	0.0615137i	−0.552326	+	0.833629i	$0.686259\pi$
$380$	−5.60808	+	9.71348i	−0.287689	+	0.498291i
$381$	−16.2042	−	15.6456i	−0.830168	−	0.801551i
$382$	−3.65533			−0.187023
$383$	−4.75807	−	8.24123i	−0.243126	−	0.421107i	0.718477	−	0.695551i	$-0.244840\pi$
$383$	−4.75807	−	8.24123i	−0.243126	−	0.421107i	−0.961603	+	0.274444i	$0.911506\pi$
$384$	10.2405	+	9.88752i	0.522585	+	0.504570i
$385$	3.34746	−	34.6391i	0.170602	−	1.76537i
$386$	0.177504	−	0.102482i	0.00903473	−	0.00521620i
$387$	−27.9672	+	0.981286i	−1.42165	+	0.0498816i
$388$	−16.8229	−	9.71271i	−0.854054	−	0.493088i
$389$			10.2200i			0.518174i	0.965854	+	0.259087i	$0.0834216\pi$
$389$			10.2200i			0.518174i	−0.965854	+	0.259087i	$0.916578\pi$
$390$	−2.61517	+	18.4558i	−0.132424	+	0.934544i
$391$		−	3.65432i		−	0.184807i
$392$	−3.44537	−	1.98918i	−0.174017	−	0.100469i
$393$	2.00708	+	0.500245i	0.101244	+	0.0252340i
$394$	1.52935	+	2.64891i	0.0770476	+	0.133450i
$395$			1.14202i			0.0574614i
$396$	−7.22996	+	10.9190i	−0.363319	+	0.548701i
$397$	25.4773	−	14.7093i	1.27867	−	0.738239i	0.302063	−	0.953288i	$-0.402325\pi$
$397$	25.4773	−	14.7093i	1.27867	−	0.738239i	0.976603	+	0.215049i	$0.0689912\pi$
$398$		−	3.56005i		−	0.178449i
$399$	−8.25723	+	8.55203i	−0.413378	+	0.428137i
$400$	−1.46365	+	2.53511i	−0.0731824	+	0.126756i
$401$	9.74398	−	16.8771i	0.486591	−	0.842801i	−0.513290	−	0.858215i	$-0.671573\pi$
$401$	9.74398	−	16.8771i	0.486591	−	0.842801i	0.999881	+	0.0154145i	$0.00490679\pi$
$402$	−2.02202	−	7.04942i	−0.100849	−	0.351593i
$403$	16.5539	−	11.9963i	0.824609	−	0.597579i
$404$	20.4087			1.01537
$405$	−18.1744	−	26.9253i	−0.903092	−	1.33793i
$406$	14.0017	+	8.08390i	0.694894	+	0.401197i
$407$	−0.357562	−	0.785318i	−0.0177237	−	0.0389268i
$408$	−2.82924	+	0.811526i	−0.140068	+	0.0401765i
$409$	−13.6097	−	23.5727i	−0.672956	−	1.16559i	−0.977062	−	0.212956i	$-0.931691\pi$
$409$	−13.6097	−	23.5727i	−0.672956	−	1.16559i	0.304105	−	0.952638i	$-0.401643\pi$
$410$	−5.04272	−	8.73424i	−0.249042	−	0.431353i
$411$	−0.759935	−	2.64938i	−0.0374848	−	0.130684i
$412$	12.3791	+	21.4413i	0.609877	+	1.05634i
$413$	−0.353240	+	0.611830i	−0.0173818	+	0.0301062i
$414$	−0.512999	−	14.6207i	−0.0252125	−	0.718569i
$415$			56.4147i			2.76929i
$416$	−19.0480	−	8.50857i	−0.933907	−	0.417167i
$417$	−11.9981	+	3.44147i	−0.587547	+	0.168529i
$418$	−3.76208	+	5.27038i	−0.184009	+	0.257783i
$419$	−19.6051	−	11.3190i	−0.957771	−	0.552969i	−0.0622847	−	0.998058i	$-0.519839\pi$
$419$	−19.6051	−	11.3190i	−0.957771	−	0.552969i	−0.895486	+	0.445089i	$0.853172\pi$
$420$	−16.6148	+	17.2080i	−0.810719	+	0.839663i
$421$		−	16.3608i		−	0.797379i	−0.917086	−	0.398689i	$-0.869465\pi$
$421$		−	16.3608i		−	0.797379i	0.917086	−	0.398689i	$-0.130535\pi$
$422$	−5.38664	−	9.32994i	−0.262218	−	0.454174i
$423$	−16.4493	−	8.74274i	−0.799792	−	0.425086i
$424$	−1.95474			−0.0949304
$425$	−2.48744	−	4.30837i	−0.120659	−	0.208987i
$426$	−5.31862	+	21.3394i	−0.257688	+	1.03390i
$427$	−23.3977	−	13.5086i	−1.13229	−	0.653729i
$428$	12.5664			0.607419
$429$	4.86503	−	20.1328i	0.234886	−	0.972023i
$430$	−27.8427			−1.34269
$431$	−2.91467	−	1.68278i	−0.140395	−	0.0810568i	0.428157	−	0.903704i	$-0.359163\pi$
$431$	−2.91467	−	1.68278i	−0.140395	−	0.0810568i	−0.568552	+	0.822647i	$0.692496\pi$
$432$	1.80179	−	0.585933i	0.0866886	−	0.0281907i
$433$	−17.9077	−	31.0170i	−0.860587	−	1.49058i	−0.871363	−	0.490639i	$-0.836763\pi$
$433$	−17.9077	−	31.0170i	−0.860587	−	1.49058i	0.0107758	−	0.999942i	$-0.496570\pi$
$434$	−13.6304			−0.654283
$435$	29.2055	−	30.2482i	1.40029	−	1.45029i
$436$	−4.38745	−	7.59928i	−0.210121	−	0.363940i
$437$			13.9230i			0.666026i
$438$	−13.6468	−	13.1763i	−0.652068	−	0.629590i
$439$	−27.7633	−	16.0291i	−1.32507	−	0.765029i	−0.340537	−	0.940231i	$-0.610609\pi$
$439$	−27.7633	−	16.0291i	−1.32507	−	0.765029i	−0.984532	+	0.175202i	$0.943942\pi$
$440$	−19.0728	+	26.7195i	−0.909259	+	1.27380i
$441$	−3.69054	+	2.30696i	−0.175740	+	0.109855i
$442$	1.49608	−	1.08418i	0.0711613	−	0.0515693i
$443$		−	16.7830i		−	0.797385i	−0.917085	−	0.398693i	$-0.869464\pi$
$443$		−	16.7830i		−	0.797385i	0.917085	−	0.398693i	$-0.130536\pi$
$444$	−0.143437	+	0.575496i	−0.00680720	+	0.0273119i
$445$	19.1166	−	33.1110i	0.906216	−	1.56961i
$446$	1.71633	+	2.97277i	0.0812705	+	0.140765i
$447$	1.24138	−	0.356070i	0.0587151	−	0.0168416i
$448$	5.89470	+	10.2099i	0.278499	+	0.482374i
$449$	2.77452	+	4.80562i	0.130938	+	0.226791i	0.924038	−	0.382300i	$-0.124868\pi$
$449$	2.77452	+	4.80562i	0.130938	+	0.226791i	−0.793101	+	0.609091i	$0.791534\pi$
$450$	−10.5569	−	16.8884i	−0.497659	−	0.796126i
$451$	4.64378	+	10.1992i	0.218667	+	0.480261i
$452$	−11.6059	−	6.70067i	−0.545896	−	0.315173i
$453$	9.17934	+	2.28786i	0.431283	+	0.107493i
$454$	6.98706			0.327919
$455$	15.4298	−	34.5426i	0.723362	−	1.61938i
$456$	10.7794	−	3.09192i	0.504792	−	0.144792i
$457$	−9.72010	+	16.8357i	−0.454687	+	0.787541i	−0.998670	−	0.0515551i	$-0.983582\pi$
$457$	−9.72010	+	16.8357i	−0.454687	+	0.787541i	0.543983	+	0.839096i	$0.316916\pi$
$458$	6.59916	−	11.4301i	0.308359	−	0.534093i
$459$	−0.668679	+	3.14975i	−0.0312113	+	0.147018i
$460$			28.0151i			1.30621i
$461$	−3.66287	+	2.11476i	−0.170597	+	0.0984940i	−0.582867	−	0.812567i	$-0.698069\pi$
$461$	−3.66287	+	2.11476i	−0.170597	+	0.0984940i	0.412270	+	0.911061i	$0.364736\pi$
$462$	−10.5032	+	8.96583i	−0.488654	+	0.417128i
$463$			1.28884i			0.0598974i	0.999551	+	0.0299487i	$0.00953439\pi$
$463$			1.28884i			0.0598974i	−0.999551	+	0.0299487i	$0.990466\pi$
$464$	1.22616	+	2.12378i	0.0569232	+	0.0985939i
$465$	−8.57275	+	34.3956i	−0.397552	+	1.59506i
$466$	10.3777	+	5.99157i	0.480738	+	0.277554i
$467$			7.43668i			0.344128i	0.985086	+	0.172064i	$0.0550437\pi$
$467$			7.43668i			0.344128i	−0.985086	+	0.172064i	$0.944956\pi$
$468$	−11.2278	+	8.75306i	−0.519003	+	0.404610i
$469$			14.8845i			0.687302i
$470$	−16.0509	−	9.26700i	−0.740374	−	0.427455i
$471$	−14.3343	−	3.57267i	−0.660489	−	0.164620i
$472$	0.577158	−	0.333222i	0.0265659	−	0.0153378i
$473$	30.7944	+	2.97592i	1.41593	+	0.136833i
$474$	0.314777	−	0.326015i	0.0144582	−	0.0149744i
$475$	9.47716	+	16.4149i	0.434842	+	0.753168i
$476$	2.37096			0.108673
$477$	−1.00363	+	1.88830i	−0.0459528	+	0.0864594i
$478$	−0.208616	+	0.361333i	−0.00954186	+	0.0165270i
$479$	−7.29276	−	4.21048i	−0.333215	−	0.192382i	0.324053	−	0.946039i	$-0.394954\pi$
$479$	−7.29276	−	4.21048i	−0.333215	−	0.192382i	−0.657267	+	0.753657i	$0.728288\pi$
$480$	34.7711	−	9.97357i	1.58708	−	0.455229i
$481$	−0.0969165	−	0.933038i	−0.00441901	−	0.0425429i
$482$		−	15.1890i		−	0.691841i
$483$	−7.18089	+	28.8112i	−0.326742	+	1.31095i
$484$	9.50587	−	10.9200i	0.432085	−	0.496363i
$485$	−46.1352	+	26.6361i	−2.09489	+	1.20948i
$486$	−2.23318	+	12.6958i	−0.101299	+	0.575895i
$487$	4.64583	−	2.68227i	0.210523	−	0.121545i	−0.391032	−	0.920377i	$-0.627882\pi$
$487$	4.64583	−	2.68227i	0.210523	−	0.121545i	0.601554	+	0.798832i	$0.294548\pi$
$488$	12.7431	+	22.0717i	0.576853	+	0.999139i
$489$	21.9751	−	6.30323i	0.993747	−	0.285042i
$490$	−3.75008	+	2.16511i	−0.169411	+	0.0978098i
$491$	−17.1649	+	29.7305i	−0.774642	+	1.34172i	0.160354	+	0.987060i	$0.448736\pi$
$491$	−17.1649	+	29.7305i	−0.774642	+	1.34172i	−0.934996	+	0.354659i	$0.884597\pi$
$492$	1.86286	−	7.47416i	0.0839841	−	0.336961i
$493$	−4.16768			−0.187703
$494$	−5.70007	+	4.13074i	−0.256458	+	0.185851i
$495$	16.0188	+	32.1432i	0.719992	+	1.44473i
$496$	−1.79048	−	1.03373i	−0.0803948	−	0.0464160i
$497$	22.3177	−	38.6555i	1.00109	−	1.73393i
$498$	15.5496	−	16.1048i	0.696796	−	0.721674i
$499$			9.37911i			0.419867i	0.977716	+	0.209933i	$0.0673247\pi$
$499$			9.37911i			0.419867i	−0.977716	+	0.209933i	$0.932675\pi$
$500$	7.19286	+	12.4584i	0.321675	+	0.557157i
$501$	−26.5706	−	25.6547i	−1.18709	−	1.14617i
$502$	10.3358			0.461309
$503$	6.38729	+	11.0631i	0.284795	+	0.493280i	0.972560	−	0.232654i	$-0.0747411\pi$
$503$	6.38729	+	11.0631i	0.284795	+	0.493280i	−0.687764	+	0.725934i	$0.741408\pi$
$504$	23.9008	−	0.838611i	1.06463	−	0.0373547i
$505$	27.9844	−	48.4704i	1.24529	−	2.15691i
$506$	−1.55575	+	16.0988i	−0.0691617	+	0.715678i
$507$	11.9769	−	19.0671i	0.531915	−	0.846798i
$508$		−	17.1163i		−	0.759413i
$509$	−9.99651	+	17.3145i	−0.443088	+	0.767450i	−0.997917	−	0.0645139i	$-0.979450\pi$
$509$	−9.99651	+	17.3145i	−0.443088	+	0.767450i	0.554829	+	0.831964i	$0.312784\pi$
$510$	−0.774772	+	3.10854i	−0.0343075	+	0.137649i
$511$	19.2505	+	33.3429i	0.851594	+	1.47500i
$512$			4.10960i			0.181620i
$513$	2.54767	−	12.0005i	0.112482	−	0.529837i
$514$	4.09244	+	7.08832i	0.180510	+	0.312652i
$515$	67.8971			2.99191
$516$	−15.2980	−	14.7707i	−0.673457	−	0.650242i
$517$	16.7621	+	11.9650i	0.737195	+	0.526221i
$518$	−0.312716	+	0.541641i	−0.0137400	+	0.0237983i
$519$	−4.80962	−	16.7679i	−0.211119	−	0.736029i
$520$	−28.8979	+	20.9418i	−1.26726	+	0.918358i
$521$			24.6791i			1.08121i	0.841276	+	0.540606i	$0.181805\pi$
$521$			24.6791i			1.08121i	−0.841276	+	0.540606i	$0.818195\pi$
$522$	−16.6747	+	0.585065i	−0.729830	+	0.0256076i
$523$	16.7524	+	9.67202i	0.732533	+	0.422928i	0.819348	−	0.573296i	$-0.194336\pi$
$523$	16.7524	+	9.67202i	0.732533	+	0.422928i	−0.0868151	+	0.996224i	$0.527669\pi$
$524$	0.785909	+	1.36123i	0.0343326	+	0.0594658i
$525$	11.1452	+	38.8558i	0.486417	+	1.69581i
$526$	7.98608	−	4.61076i	0.348210	−	0.201039i
$527$	3.04288	−	1.75681i	0.132550	−	0.0765277i
$528$	−2.05966	+	0.381175i	−0.0896351	+	0.0165885i
$529$	5.88799	+	10.1983i	0.256000	+	0.443404i
$530$	−1.06381	+	1.84257i	−0.0462089	+	0.0800361i
$531$	−0.0255655	−	0.728630i	−0.00110945	−	0.0316198i
$532$	−9.03338			−0.391647
$533$	1.25869	+	12.1177i	0.0545198	+	0.524875i
$534$	−14.5837	+	4.18311i	−0.631097	+	0.181021i
$535$	17.2310	−	29.8450i	0.744962	−	1.29031i
$536$	7.02049	−	12.1599i	0.303239	−	0.525226i
$537$	13.0168	+	12.5681i	0.561716	+	0.542353i
$538$	−0.188348			−0.00812027
$539$	4.37906	−	1.99383i	0.188620	−	0.0858801i
$540$	5.12630	−	24.1469i	0.220601	−	1.03912i
$541$	3.98233			0.171214			0.0856068	−	0.996329i	$-0.472717\pi$
$541$	3.98233			0.171214			0.0856068	+	0.996329i	$0.472717\pi$
$542$	−3.66867	+	2.11811i	−0.157583	+	0.0909805i
$543$	−29.7759	−	7.42134i	−1.27781	−	0.318480i
$544$	−3.10514	−	1.79275i	−0.133132	−	0.0768637i
$545$	−24.0643			−1.03080
$546$	−13.9258	+	5.60799i	−0.595969	+	0.240000i
$547$			15.7154i			0.671940i	0.941873	+	0.335970i	$0.109064\pi$
$547$			15.7154i			0.671940i	−0.941873	+	0.335970i	$0.890936\pi$
$548$	1.04721	−	1.81382i	0.0447345	−	0.0774824i
$549$	27.8643	−	0.977677i	1.18922	−	0.0417262i
$550$	9.12399	+	20.0391i	0.389048	+	0.854472i
$551$	15.8789			0.676463
$552$	19.4556	−	20.1503i	0.828087	−	0.857652i
$553$	−0.796547	+	0.459887i	−0.0338726	+	0.0195564i
$554$	0.779086			0.0331002
$555$	1.17012	+	1.12978i	0.0496687	+	0.0479565i
$556$	−8.21411	−	4.74242i	−0.348356	−	0.201123i
$557$	1.76818	+	1.02086i	0.0749202	+	0.0432552i	0.536992	−	0.843587i	$-0.319560\pi$
$557$	1.76818	+	1.02086i	0.0749202	+	0.0432552i	−0.462072	+	0.886842i	$0.652894\pi$
$558$	11.9278	−	7.45605i	0.504943	−	0.315640i
$559$	30.7086	+	13.7172i	1.29884	+	0.580177i
$560$	−3.82596			−0.161676
$561$	1.18916	−	3.35528i	0.0502064	−	0.141660i
$562$	−7.32040	+	12.6793i	−0.308792	+	0.534844i
$563$	−17.5130	−	30.3335i	−0.738087	−	1.27840i	−0.953356	−	0.301849i	$-0.902396\pi$
$563$	−17.5130	−	30.3335i	−0.738087	−	1.27840i	0.215269	−	0.976555i	$-0.430937\pi$
$564$	−3.90290	−	13.6068i	−0.164342	−	0.572949i
$565$	−31.8280	+	18.3759i	−1.33901	+	0.773080i
$566$	−1.97645	−	3.42330i	−0.0830762	−	0.143892i
$567$	11.4614	−	23.5191i	0.481332	−	0.987709i
$568$	−36.4649	+	21.0530i	−1.53003	+	0.883365i
$569$	0.907095	−	1.57113i	0.0380274	−	0.0658654i	−0.846385	−	0.532571i	$-0.821226\pi$
$569$	0.907095	−	1.57113i	0.0380274	−	0.0658654i	0.884413	+	0.466706i	$0.154559\pi$
$570$	2.95189	−	11.8436i	0.123641	−	0.496072i
$571$			7.01838i			0.293710i	0.989158	+	0.146855i	$0.0469151\pi$
$571$			7.01838i			0.293710i	−0.989158	+	0.146855i	$0.953085\pi$
$572$	13.5737	−	7.96695i	0.567546	−	0.333115i
$573$	−7.35941	+	2.11094i	−0.307444	+	0.0881858i
$574$	4.06135	−	7.03447i	0.169518	−	0.293613i
$575$	41.0003	+	23.6715i	1.70983	+	0.987170i
$576$	−10.7433	−	5.71004i	−0.447639	−	0.237918i
$577$			35.3698i			1.47247i	0.676728	+	0.736233i	$0.263397\pi$
$577$			35.3698i			1.47247i	−0.676728	+	0.736233i	$0.736603\pi$
$578$	−11.8996	+	6.87023i	−0.494958	+	0.285764i
$579$	0.298193	−	0.308839i	0.0123925	−	0.0128349i
$580$	31.9507			1.32668
$581$	−39.3486	+	22.7179i	−1.63245	+	0.942498i
$582$	20.5120	+	5.11241i	0.850251	+	0.211916i
$583$	1.37353	−	1.92421i	0.0568857	−	0.0796925i
$584$		−	36.3192i		−	1.50290i
$585$	5.39292	+	38.6680i	0.222970	+	1.59872i
$586$	14.0386			0.579929
$587$	−0.294905	+	0.510791i	−0.0121720	+	0.0210826i	−0.872047	−	0.489422i	$-0.837208\pi$
$587$	−0.294905	+	0.510791i	−0.0121720	+	0.0210826i	0.859875	+	0.510504i	$0.170541\pi$
$588$	−3.20906	−	0.799826i	−0.132340	−	0.0329843i
$589$	−11.5934	+	6.69344i	−0.477697	+	0.275798i
$590$		−	0.725386i		−	0.0298637i
$591$	4.60884	+	4.44996i	0.189582	+	0.183047i
$592$	−0.0821560	+	0.0474328i	−0.00337659	+	0.00194948i
$593$			44.3988i			1.82324i	0.411034	+	0.911620i	$0.365168\pi$
$593$			44.3988i			1.82324i	−0.411034	+	0.911620i	$0.634832\pi$
$594$	4.28675	−	13.5913i	0.175888	−	0.557656i
$595$	3.25106	−	5.63101i	0.133281	−	0.230849i
$596$	0.849871	+	0.490673i	0.0348121	+	0.0200988i
$597$	−2.05592	−	7.16759i	−0.0841431	−	0.293350i
$598$	−7.17112	+	16.0539i	−0.293249	+	0.656493i
$599$			22.1393i			0.904586i	0.891869	+	0.452293i	$0.149394\pi$
$599$			22.1393i			0.904586i	−0.891869	+	0.452293i	$0.850606\pi$
$600$	9.22187	−	37.0000i	0.376481	−	1.51052i
$601$	−29.7118	−	17.1541i	−1.21197	−	0.699730i	−0.248781	−	0.968560i	$-0.580030\pi$
$601$	−29.7118	−	17.1541i	−1.21197	−	0.699730i	−0.963188	+	0.268829i	$0.913363\pi$
$602$	−11.2121	−	19.4199i	−0.456971	−	0.791497i
$603$	−8.14203	−	13.0252i	−0.331569	−	0.530425i
$604$	3.59434	+	6.22557i	0.146251	+	0.253315i
$605$	−12.9004	−	37.5498i	−0.524475	−	1.52662i
$606$	−21.3487	+	6.12357i	−0.867232	+	0.248753i
$607$	−12.5059	+	7.22028i	−0.507599	+	0.293062i	−0.731846	−	0.681470i	$-0.761341\pi$
$607$	−12.5059	+	7.22028i	−0.507599	+	0.293062i	0.224247	+	0.974532i	$0.428008\pi$
$608$	11.8306	+	6.83041i	0.479795	+	0.277010i
$609$	32.8586	+	8.18968i	1.33150	+	0.331862i
$610$	27.7403			1.12317
$611$	13.1375	+	18.1287i	0.531487	+	0.733407i
$612$	−2.07479	+	1.29695i	−0.0838684	+	0.0524261i
$613$	−6.24909	+	10.8237i	−0.252398	+	0.437167i	−0.964186	−	0.265228i	$-0.914553\pi$
$613$	−6.24909	+	10.8237i	−0.252398	+	0.437167i	0.711787	+	0.702395i	$0.247886\pi$
$614$	19.1665	+	11.0658i	0.773495	+	0.446578i
$615$	−15.1967	−	14.6728i	−0.612790	−	0.591666i
$616$	−26.3170	−	2.54323i	−1.06034	−	0.102470i
$617$	7.25971	+	12.5742i	0.292265	+	0.506218i	0.974345	−	0.225060i	$-0.0722577\pi$
$617$	7.25971	+	12.5742i	0.292265	+	0.506218i	−0.682080	+	0.731278i	$0.738924\pi$
$618$	−19.3827	−	18.7146i	−0.779687	−	0.752810i
$619$			28.1176i			1.13014i	0.825042	+	0.565071i	$0.191151\pi$
$619$			28.1176i			1.13014i	−0.825042	+	0.565071i	$0.808849\pi$
$620$	−23.3276	+	13.4682i	−0.936860	+	0.540896i
$621$	−9.47626	−	29.1402i	−0.380269	−	1.16936i
$622$	0.180752	−	0.313072i	0.00724751	−	0.0125531i
$623$	30.7927			1.23368
$624$	−2.25458	−	0.319473i	−0.0902555	−	0.0127891i
$625$	−0.689408			−0.0275763
$626$	10.0443	+	5.79911i	0.401453	+	0.231779i
$627$	−4.53071	+	12.7837i	−0.180939	+	0.510530i
$628$	−5.61285	−	9.72174i	−0.223977	−	0.387940i
$629$		−	0.161222i		−	0.00642834i
$630$	12.2168	−	22.9858i	0.486731	−	0.915775i
$631$	40.8299	−	23.5731i	1.62541	−	0.938432i	0.639975	−	0.768396i	$-0.278945\pi$
$631$	40.8299	−	23.5731i	1.62541	−	0.938432i	0.985438	−	0.170036i	$-0.0543885\pi$
$632$	0.867650			0.0345133
$633$	−16.2331	−	15.6736i	−0.645209	−	0.622968i
$634$	−0.947270	−	0.546907i	−0.0376209	−	0.0217204i
$635$	−40.6510	−	23.4699i	−1.61319	−	0.931373i
$636$	−1.56199	+	0.448035i	−0.0619371	+	0.0177657i
$637$	5.20277	−	0.540422i	0.206141	−	0.0214123i
$638$	18.3603	+	1.77431i	0.726893	+	0.0702456i
$639$	1.61523	+	46.0349i	0.0638975	+	1.82111i
$640$	25.6901	+	14.8322i	1.01549	+	0.586292i
$641$	15.6699	−	9.04702i	0.618924	−	0.357336i	−0.157526	−	0.987515i	$-0.550352\pi$
$641$	15.6699	−	9.04702i	0.618924	−	0.357336i	0.776450	+	0.630179i	$0.217018\pi$
$642$	−13.1452	+	3.77050i	−0.518798	+	0.148810i
$643$	39.2511	−	22.6617i	1.54791	−	0.893688i	0.549613	−	0.835420i	$-0.314775\pi$
$643$	39.2511	−	22.6617i	1.54791	−	0.893688i	0.998301	−	0.0582687i	$-0.0185580\pi$
$644$	−19.5402	+	11.2815i	−0.769992	+	0.444555i
$645$	−56.0567	+	16.0790i	−2.20723	+	0.633112i
$646$	−1.04777	+	0.604927i	−0.0412238	+	0.0238006i
$647$	−9.09155	−	5.24901i	−0.357426	−	0.206360i	0.310525	−	0.950565i	$-0.399495\pi$
$647$	−9.09155	−	5.24901i	−0.357426	−	0.206360i	−0.667951	+	0.744205i	$0.732828\pi$
$648$	−20.4565	+	13.8080i	−0.803606	+	0.542428i
$649$	−0.0775317	+	0.802289i	−0.00304338	+	0.0314926i
$650$	2.47304	+	23.8085i	0.0970006	+	0.933848i
$651$	−27.4427	+	7.87154i	−1.07556	+	0.308510i
$652$	15.0446	+	8.68599i	0.589191	+	0.340170i
$653$	−39.1789	−	22.6199i	−1.53319	−	0.885186i	−0.999212	−	0.0396861i	$-0.987364\pi$
$653$	−39.1789	−	22.6199i	−1.53319	−	0.885186i	−0.533975	−	0.845500i	$-0.679302\pi$
$654$	6.86967	+	6.63286i	0.268625	+	0.259365i
$655$	4.31055			0.168427
$656$	1.06699	−	0.616025i	0.0416588	−	0.0240517i
$657$	−35.0849	−	18.6475i	−1.36879	−	0.727507i
$658$		−	14.9271i		−	0.581919i
$659$	8.74287	+	15.1431i	0.340574	+	0.589891i	0.984539	−	0.175163i	$-0.0560453\pi$
$659$	8.74287	+	15.1431i	0.340574	+	0.589891i	−0.643966	+	0.765055i	$0.722712\pi$
$660$	−9.11647	+	25.7226i	−0.354858	+	1.00125i
$661$	20.8361	+	12.0297i	0.810430	+	0.467902i	0.847105	−	0.531425i	$-0.178343\pi$
$661$	20.8361	+	12.0297i	0.810430	+	0.467902i	−0.0366754	+	0.999327i	$0.511677\pi$
$662$	18.5645			0.721531
$663$	2.38600	−	3.04681i	0.0926647	−	0.118328i
$664$	42.8610			1.66333
$665$	−12.3866	+	21.4542i	−0.480331	+	0.831957i
$666$	−0.0226326	−	0.645041i	−0.000876996	−	0.0249948i
$667$	34.3477	−	19.8307i	1.32995	−	0.767847i
$668$		−	28.0662i		−	1.08591i
$669$	5.17231	+	4.99402i	0.199973	+	0.193080i
$670$	−7.64140	−	13.2353i	−0.295213	−	0.511324i
$671$	−30.6812	−	2.96497i	−1.18443	−	0.114461i
$672$	20.9586	+	20.2361i	0.808495	+	0.780625i
$673$	20.5488	+	11.8638i	0.792097	+	0.457317i	0.840700	−	0.541501i	$-0.182144\pi$
$673$	20.5488	+	11.8638i	0.792097	+	0.457317i	−0.0486035	+	0.998818i	$0.515477\pi$
$674$	−5.84008	+	10.1153i	−0.224952	+	0.389627i
$675$	−31.0077	−	27.9054i	−1.19349	−	1.07408i
$676$	16.7449	−	3.51659i	0.644034	−	0.135254i
$677$	10.8608			0.417414			0.208707	−	0.977978i	$-0.433074\pi$
$677$	10.8608			0.417414			0.208707	+	0.977978i	$0.433074\pi$
$678$	14.1510	+	3.52698i	0.543465	+	0.135453i
$679$	−37.1568	−	21.4525i	−1.42595	−	0.823270i
$680$	−5.31190	+	3.06683i	−0.203702	+	0.117607i
$681$	14.0673	−	4.03500i	0.539061	−	0.154622i
$682$	−14.1531	+	6.44401i	−0.541948	+	0.246754i
$683$	16.4670	+	28.5216i	0.630091	+	1.09135i	0.987533	+	0.157414i	$0.0503158\pi$
$683$	16.4670	+	28.5216i	0.630091	+	1.09135i	−0.357442	+	0.933935i	$0.616351\pi$
$684$	7.90496	−	4.94139i	0.302254	−	0.188939i
$685$	−2.87186	−	4.97421i	−0.109728	−	0.190055i
$686$	11.5528	+	6.67002i	0.441088	+	0.254662i
$687$	6.68551	−	26.8236i	0.255068	−	1.02339i
$688$		−	3.40130i		−	0.129673i
$689$	2.08109	−	1.50813i	0.0792831	−	0.0574550i
$690$	−8.40584	−	29.3054i	−0.320005	−	1.11564i
$691$	−7.96732	−	4.59993i	−0.303091	−	0.174990i	0.340740	−	0.940158i	$-0.389323\pi$
$691$	−7.96732	−	4.59993i	−0.303091	−	0.174990i	−0.643831	+	0.765168i	$0.722656\pi$
$692$	6.62777	−	11.4796i	0.251950	−	0.436390i
$693$	−15.9688	+	24.1168i	−0.606605	+	0.916123i
$694$		−	19.5004i		−	0.740224i
$695$	−22.5264	+	13.0056i	−0.854474	+	0.493331i
$696$	−22.9810	−	22.1888i	−0.871093	−	0.841064i
$697$			2.09384i			0.0793099i
$698$	17.4877	−	10.0965i	0.661917	−	0.382158i
$699$	24.3540	+	6.06998i	0.921151	+	0.229588i
$700$	−15.3584	+	26.6015i	−0.580491	+	1.00544i
$701$	−38.1047			−1.43919			−0.719597	−	0.694392i	$-0.755673\pi$
$701$	−38.1047			−1.43919			−0.719597	+	0.694392i	$0.755673\pi$
$702$	9.11856	−	12.5251i	0.344158	−	0.472728i
$703$			0.614257i			0.0231671i
$704$	10.9476	+	7.81457i	0.412604	+	0.294523i
$705$	−37.6676	−	9.38826i	−1.41864	−	0.353582i
$706$	−6.66308	+	3.84693i	−0.250768	+	0.144781i
$707$	45.0767			1.69529
$708$	0.384821	−	0.398560i	0.0144624	−	0.0149788i
$709$	−39.8120	+	22.9855i	−1.49517	+	0.863238i	−0.999985	−	0.00554755i	$-0.998234\pi$
$709$	−39.8120	+	22.9855i	−1.49517	+	0.863238i	−0.495188	+	0.868786i	$0.664901\pi$
$710$			45.8299i			1.71997i
$711$	0.445480	−	0.838162i	0.0167068	−	0.0314335i
$712$	−25.1560	−	14.5238i	−0.942762	−	0.544304i
$713$	−16.7185	+	28.9573i	−0.626112	+	1.08446i
$714$	−2.48017	+	0.711400i	−0.0928179	+	0.0266235i
$715$	−0.309123	−	43.1617i	−0.0115606	−	1.61416i
$716$			13.7495i			0.513841i
$717$	−0.211346	+	0.847961i	−0.00789285	+	0.0316677i
$718$	2.07789	−	3.59902i	0.0775463	−	0.134314i
$719$	14.7218	−	8.49963i	0.549030	−	0.316983i	−0.199701	−	0.979857i	$-0.563997\pi$
$719$	14.7218	−	8.49963i	0.549030	−	0.316983i	0.748731	+	0.662874i	$0.230664\pi$
$720$	3.34803	−	2.09285i	0.124774	−	0.0779960i
$721$	27.3418	+	47.3574i	1.01826	+	1.76368i
$722$	−9.61491	+	5.55117i	−0.357830	+	0.206593i
$723$	−8.77161	−	30.5807i	−0.326220	−	1.13731i
$724$	−11.6593	−	20.1945i	−0.433314	−	0.750522i
$725$	26.9969	−	46.7600i	1.00264	−	1.73662i
$726$	−6.66719	+	14.2752i	−0.247443	+	0.529801i
$727$	10.6367			0.394494			0.197247	−	0.980354i	$-0.436800\pi$
$727$	10.6367			0.394494			0.197247	+	0.980354i	$0.436800\pi$
$728$	−26.2437	−	11.7228i	−0.972656	−	0.434476i
$729$	2.83565	+	26.8507i	0.105024	+	0.994470i
$730$	−34.2352	−	19.7657i	−1.26710	−	0.731561i
$731$	5.00600	+	2.89022i	0.185154	+	0.106899i
$732$	15.2417	+	14.7163i	0.563351	+	0.543931i
$733$	0.903764			0.0333813			0.0166906	−	0.999861i	$-0.494687\pi$
$733$	0.903764			0.0333813			0.0166906	+	0.999861i	$0.494687\pi$
$734$	15.6801	−	9.05289i	0.578762	−	0.334148i
$735$	−6.29984	+	6.52476i	−0.232373	+	0.240669i
$736$	34.1212			1.25772
$737$	7.03687	+	15.4552i	0.259207	+	0.569299i
$738$	0.293937	+	8.37736i	0.0108200	+	0.308375i
$739$	23.8682	−	41.3409i	0.878006	−	1.52075i	0.0244805	−	0.999700i	$-0.492207\pi$
$739$	23.8682	−	41.3409i	0.878006	−	1.52075i	0.853526	−	0.521051i	$-0.174460\pi$
$740$			1.23598i			0.0454354i
$741$	−9.09069	+	11.6083i	−0.333955	+	0.426443i
$742$	−1.71356			−0.0629068
$743$	0.724160	+	0.418094i	0.0265668	+	0.0153384i	0.513225	−	0.858254i	$-0.328451\pi$
$743$	0.724160	+	0.418094i	0.0265668	+	0.0153384i	−0.486658	+	0.873593i	$0.661784\pi$
$744$	26.1320	+	6.51313i	0.958045	+	0.238783i
$745$	2.33069	−	1.34562i	0.0853897	−	0.0492998i
$746$	−16.8905			−0.618405
$747$	22.0062	−	41.4043i	0.805166	−	1.51490i
$748$	2.46187	−	1.12091i	0.0900148	−	0.0409845i
$749$	27.7554			1.01416
$750$	−11.2623	−	10.8740i	−0.411240	−	0.397063i
$751$	−11.3098	+	19.5892i	−0.412701	+	0.714819i	−0.995184	−	0.0980237i	$-0.968748\pi$
$751$	−11.3098	+	19.5892i	−0.412701	+	0.714819i	0.582483	+	0.812843i	$0.302081\pi$
$752$	1.13207	−	1.96080i	0.0412823	−	0.0715031i
$753$	20.8094	−	5.96888i	0.758338	−	0.217518i
$754$	18.3092	+	8.17853i	0.666781	+	0.297844i
$755$	19.7142			0.717473
$756$	18.9065	−	6.14831i	0.687624	−	0.223612i
$757$	−9.88087	+	17.1142i	−0.359126	+	0.622025i	−0.987815	−	0.155632i	$-0.950259\pi$
$757$	−9.88087	+	17.1142i	−0.359126	+	0.622025i	0.628689	+	0.777657i	$0.283592\pi$
$758$	0.990299	+	1.71525i	0.0359693	+	0.0623006i
$759$	6.16472	+	33.3107i	0.223765	+	1.20910i
$760$	20.2384	−	11.6846i	0.734123	−	0.423846i
$761$	31.4569	−	18.1616i	1.14031	−	0.658358i	0.193803	−	0.981041i	$-0.437918\pi$
$761$	31.4569	−	18.1616i	1.14031	−	0.658358i	0.946507	+	0.322682i	$0.104584\pi$
$762$	5.13569	+	17.9047i	0.186046	+	0.648617i
$763$	−9.69056	−	16.7845i	−0.350822	−	0.607641i
$764$	−5.03840	−	2.90892i	−0.182283	−	0.105241i
$765$	0.235293	+	6.70598i	0.00850704	+	0.242455i
$766$			7.86930i			0.284330i
$767$	−0.357375	+	0.800053i	−0.0129041	+	0.0288882i
$768$	−7.11904	−	24.8192i	−0.256886	−	0.895588i
$769$	7.14901	−	12.3825i	0.257800	−	0.446523i	−0.707852	−	0.706360i	$-0.750336\pi$
$769$	7.14901	−	12.3825i	0.257800	−	0.446523i	0.965652	+	0.259838i	$0.0836691\pi$
$770$	−16.7196	+	23.4228i	−0.602532	+	0.844101i
$771$	12.3330	+	11.9078i	0.444160	+	0.428849i
$772$	0.326222			0.0117410
$773$	12.6620	+	21.9313i	0.455421	+	0.788813i	0.998712	−	0.0507315i	$-0.0161553\pi$
$773$	12.6620	+	21.9313i	0.455421	+	0.788813i	−0.543291	+	0.839545i	$0.682822\pi$
$774$	20.4345	+	10.8609i	0.734503	+	0.390385i
$775$			45.5201i			1.63513i
$776$	20.2368	+	35.0511i	0.726458	+	1.25826i
$777$	−0.316808	+	1.27110i	−0.0113654	+	0.0456004i
$778$	4.22567	−	7.31907i	0.151498	−	0.262401i
$779$		−	7.97755i		−	0.285825i
$780$	−18.2918	+	23.3578i	−0.654953	+	0.836342i
$781$	4.89845	−	50.6886i	0.175280	−	1.81378i
$782$	−1.51095	+	2.61705i	−0.0540316	+	0.0935855i
$783$	−33.2339	+	10.8075i	−1.18768	+	0.386228i
$784$	−0.264493	−	0.458115i	−0.00944618	−	0.0163613i
$785$	−30.7853			−1.09878
$786$	−1.23054	−	1.18812i	−0.0438919	−	0.0423789i
$787$	24.5633	+	42.5448i	0.875586	+	1.51656i	0.856137	+	0.516749i	$0.172858\pi$
$787$	24.5633	+	42.5448i	0.875586	+	1.51656i	0.0194488	+	0.999811i	$0.493809\pi$
$788$			4.86825i			0.173424i
$789$	13.4160	−	13.8950i	0.477621	−	0.494674i
$790$	0.472193	−	0.817863i	0.0167999	−	0.0290983i
$791$	−25.6339	−	14.7998i	−0.911438	−	0.526219i
$792$	24.4208	−	12.1703i	0.867754	−	0.432451i
$793$	−30.5956	−	13.6668i	−1.08648	−	0.485321i
$794$	−24.3275			−0.863350
$795$	−1.07773	+	4.32406i	−0.0382231	+	0.153359i
$796$	2.83310	−	4.90708i	0.100417	−	0.173927i
$797$	0.534561	−	0.308629i	0.0189351	−	0.0109322i	−0.490503	−	0.871440i	$-0.663187\pi$
$797$	0.534561	−	0.308629i	0.0189351	−	0.0109322i	0.509438	+	0.860508i	$0.329853\pi$
$798$	9.44945	−	2.71044i	0.334507	−	0.0959484i
$799$	1.92393	+	3.33234i	0.0680637	+	0.117890i
$800$	40.2283	−	23.2258i	1.42228	−	0.821156i
$801$	−26.9461	+	16.8440i	−0.952095	+	0.595155i
$802$	−13.9564	+	8.05771i	−0.492816	+	0.284528i
$803$	35.7520	+	25.5203i	1.26166	+	0.900592i
$804$	2.82285	−	11.3259i	0.0995544	−	0.399432i
$805$			61.8770i			2.18088i
$806$	−16.8153	+	1.74664i	−0.592293	+	0.0615226i
$807$	−0.379209	+	0.108770i	−0.0133488	+	0.00382890i
$808$	−36.8253	−	21.2611i	−1.29551	−	0.747964i
$809$	8.26616	−	14.3174i	0.290623	−	0.503373i	−0.683334	−	0.730105i	$-0.739471\pi$
$809$	8.26616	−	14.3174i	0.290623	−	0.503373i	0.973957	+	0.226732i	$0.0728042\pi$
$810$	1.88279	+	26.7972i	0.0661546	+	0.941559i
$811$	−26.7650			−0.939846			−0.469923	−	0.882707i	$-0.655718\pi$
$811$	−26.7650			−0.939846			−0.469923	+	0.882707i	$0.655718\pi$
$812$	12.8664	+	22.2852i	0.451522	+	0.782058i
$813$	−6.16307	+	6.38311i	−0.216148	+	0.223865i
$814$	−0.0686372	+	0.710249i	−0.00240573	+	0.0248942i
$815$	41.2582	−	23.8205i	1.44521	−	0.834394i
$816$	−0.379744	−	0.0946473i	−0.0132937	−	0.00331332i
$817$	−19.0729	−	11.0117i	−0.667276	−	0.385252i
$818$			22.5089i			0.787004i
$819$	−24.7987	+	19.3329i	−0.866538	+	0.675546i
$820$		−	16.0520i		−	0.560562i
$821$	13.7604	+	7.94457i	0.480241	+	0.277268i	0.720517	−	0.693437i	$-0.243905\pi$
$821$	13.7604	+	7.94457i	0.480241	+	0.277268i	−0.240276	+	0.970705i	$0.577238\pi$
$822$	−0.551211	+	2.21157i	−0.0192257	+	0.0771374i
$823$	11.3951	+	19.7368i	0.397207	+	0.687982i	0.993380	−	0.114873i	$-0.0366463\pi$
$823$	11.3951	+	19.7368i	0.397207	+	0.687982i	−0.596173	+	0.802856i	$0.703313\pi$
$824$		−	51.5847i		−	1.79704i
$825$	29.9422	+	35.0765i	1.04245	+	1.22121i
$826$	0.505948	−	0.292109i	0.0176042	−	0.0101638i
$827$		−	20.8987i		−	0.726718i	−0.931649	−	0.363359i	$-0.881630\pi$
$827$		−	20.8987i		−	0.726718i	0.931649	−	0.363359i	$-0.118370\pi$
$828$	10.9281	−	20.5610i	0.379778	−	0.714546i
$829$	1.27661	−	2.21115i	0.0443384	−	0.0767963i	−0.843005	−	0.537906i	$-0.819215\pi$
$829$	1.27661	−	2.21115i	0.0443384	−	0.0767963i	0.887343	+	0.461110i	$0.152549\pi$
$830$	23.3259	−	40.4016i	0.809652	−	1.40236i
$831$	1.56856	−	0.449919i	0.0544129	−	0.0156075i
$832$	8.58035	+	11.8402i	0.297470	+	0.410484i
$833$	0.899000			0.0311485
$834$	10.0154	+	2.49623i	0.346805	+	0.0864375i
$835$	−66.6568	−	38.4843i	−2.30675	−	1.33180i
$836$	−9.37973	+	4.27067i	−0.324405	+	0.147704i
$837$	19.7088	−	21.8998i	0.681235	−	0.756968i
$838$	9.36016	+	16.2123i	0.323341	+	0.560044i
$839$	−26.0038	−	45.0399i	−0.897751	−	1.55495i	−0.830362	−	0.557224i	$-0.811867\pi$
$839$	−26.0038	−	45.0399i	−0.897751	−	1.55495i	−0.0673887	−	0.997727i	$-0.521467\pi$
$840$	47.9063	−	13.7412i	1.65292	−	0.474117i
$841$	−8.11652	−	14.0582i	−0.279880	−	0.484766i
$842$	−6.76474	+	11.7169i	−0.233128	+	0.403790i
$843$	−7.41619	+	29.7552i	−0.255427	+	1.02482i
$844$		−	17.1468i		−	0.590218i
$845$	14.6087	−	44.5909i	0.502555	−	1.53397i
$846$	8.16533	+	13.0624i	0.280730	+	0.449096i
$847$	20.9956	−	24.1190i	0.721418	−	0.828738i
$848$	−0.225091	−	0.129956i	−0.00772965	−	0.00446272i
$849$	−5.95620	−	5.75088i	−0.204416	−	0.197370i
$850$			4.11394i			0.141107i
$851$	0.767128	+	1.32870i	0.0262968	+	0.0455474i
$852$	−24.3130	+	25.1810i	−0.832949	+	0.862687i
$853$	−36.8393			−1.26135			−0.630677	−	0.776045i	$-0.717223\pi$
$853$	−36.8393			−1.26135			−0.630677	+	0.776045i	$0.717223\pi$
$854$	11.1709	+	19.3485i	0.382259	+	0.662092i
$855$	−0.896468	−	25.5498i	−0.0306586	−	0.873785i
$856$	−22.6747	−	13.0912i	−0.775005	−	0.447449i
$857$	−38.8835			−1.32823			−0.664117	−	0.747629i	$-0.731192\pi$
$857$	−38.8835			−1.32823			−0.664117	+	0.747629i	$0.731192\pi$
$858$	−11.8085	+	12.4066i	−0.403134	+	0.423556i
$859$	−32.7312			−1.11677			−0.558387	−	0.829581i	$-0.688580\pi$
$859$	−32.7312			−1.11677			−0.558387	+	0.829581i	$0.688580\pi$
$860$	−38.3776	−	22.1573i	−1.30866	−	0.755557i
$861$	4.11450	−	16.5082i	0.140222	−	0.562597i
$862$	1.39156	+	2.41026i	0.0473969	+	0.0820938i
$863$	−25.4617			−0.866726			−0.433363	−	0.901219i	$-0.642673\pi$
$863$	−25.4617			−0.866726			−0.433363	+	0.901219i	$0.642673\pi$
$864$	−29.4099	−	6.24361i	−1.00055	−	0.212412i
$865$	−18.1760	−	31.4817i	−0.618002	−	1.07041i
$866$			29.6172i			1.00643i
$867$	−19.9904	+	20.7041i	−0.678909	+	0.703148i
$868$	−18.7878	−	10.8472i	−0.637701	−	0.368177i
$869$	−0.609669	+	0.854099i	−0.0206816	+	0.0289733i
$870$	−33.4223	+	9.58670i	−1.13312	+	0.325020i
$871$	1.90733	+	18.3623i	0.0646275	+	0.622184i
$872$			18.2828i			0.619134i
$873$	44.2501	−	1.55261i	1.49764	−	0.0525477i
$874$	5.75674	−	9.97097i	0.194725	−	0.337273i
$875$	15.8869	+	27.5169i	0.537075	+	0.930240i
$876$	−8.32455	−	29.0220i	−0.281260	−	0.980564i
$877$	−3.21508	−	5.56869i	−0.108566	−	0.188041i	0.806624	−	0.591065i	$-0.201292\pi$
$877$	−3.21508	−	5.56869i	−0.108566	−	0.188041i	−0.915189	+	0.403024i	$0.867959\pi$
$878$	13.2552	+	22.9586i	0.447340	+	0.774816i
$879$	28.2644	−	8.10724i	0.953336	−	0.273450i
$880$	−3.97265	+	1.80878i	−0.133918	+	0.0609740i
$881$	−4.66499	−	2.69334i	−0.157168	−	0.0907408i	0.419353	−	0.907823i	$-0.362257\pi$
$881$	−4.66499	−	2.69334i	−0.157168	−	0.0907408i	−0.576521	+	0.817082i	$0.695590\pi$
$882$	3.59685	−	0.126203i	0.121112	−	0.00424948i
$883$	−1.74325			−0.0586651			−0.0293326	−	0.999570i	$-0.509338\pi$
$883$	−1.74325			−0.0586651			−0.0293326	+	0.999570i	$0.509338\pi$
$884$	2.92495	−	0.303821i	0.0983767	−	0.0102186i
$885$	−0.418908	−	1.46045i	−0.0140814	−	0.0490924i
$886$	−6.93929	+	12.0192i	−0.233130	+	0.403793i
$887$	−24.6417	+	42.6807i	−0.827388	+	1.43308i	0.0726924	+	0.997354i	$0.476841\pi$
$887$	−24.6417	+	42.6807i	−0.827388	+	1.43308i	−0.900080	+	0.435724i	$0.856492\pi$
$888$	0.858349	−	0.888994i	0.0288043	−	0.0298327i
$889$		−	37.8048i		−	1.26793i
$890$	−27.3809	+	15.8084i	−0.917809	+	0.529897i
$891$	0.781779	−	29.8394i	0.0261906	−	0.999657i
$892$			5.46344i			0.182930i
$893$	−7.33018	−	12.6962i	−0.245295	−	0.424863i
$894$	−1.03624	−	0.258272i	−0.0346570	−	0.00863791i
$895$	32.6548	+	18.8532i	1.09153	+	0.630195i
$896$			23.8913i			0.798153i
$897$	−5.16682	+	36.4632i	−0.172515	+	1.21747i
$898$		−	4.58874i		−	0.153128i
$899$	33.0252	+	19.0671i	1.10145	+	0.635924i
$900$	−1.11155	−	31.6797i	−0.0370516	−	1.05599i
$901$	0.382537	−	0.220858i	0.0127442	−	0.00735784i
$902$	0.891414	−	9.22424i	0.0296808	−	0.307134i
$903$	−33.7887	−	32.6239i	−1.12442	−	1.08566i
$904$	13.9611	+	24.1813i	0.464338	+	0.804257i
$905$	−63.9488			−2.12573
$906$	−5.62785	−	5.43385i	−0.186973	−	0.180527i
$907$	3.86028	−	6.68620i	0.128179	−	0.222012i	−0.794792	−	0.606881i	$-0.792420\pi$
$907$	3.86028	−	6.68620i	0.128179	−	0.222012i	0.922971	+	0.384870i	$0.125754\pi$
$908$	9.63077	+	5.56033i	0.319608	+	0.184526i
$909$	−39.4459	+	24.6576i	−1.30834	+	0.817842i
$910$	−25.3325	+	18.3580i	−0.839764	+	0.608562i
$911$		−	12.0195i		−	0.398225i	−0.979977	−	0.199113i	$-0.936194\pi$
$911$		−	12.0195i		−	0.398225i	0.979977	−	0.199113i	$-0.0638060\pi$
$912$	1.44683	+	0.360607i	0.0479092	+	0.0119409i
$913$	−30.1170	+	42.1916i	−0.996727	+	1.39634i
$914$	13.9222	−	8.03796i	0.460504	−	0.265872i
$915$	55.8505	−	16.0199i	1.84636	−	0.529602i
$916$	18.1922	−	10.5033i	0.601087	−	0.347038i
$917$	1.73584	+	3.00656i	0.0573224	+	0.0992853i
$918$	1.78121	−	1.97922i	0.0587885	−	0.0653240i
$919$	−1.02543	+	0.592032i	−0.0338258	+	0.0195293i	−0.516818	−	0.856096i	$-0.672883\pi$
$919$	−1.02543	+	0.592032i	−0.0338258	+	0.0195293i	0.482992	+	0.875625i	$0.339550\pi$
$920$	29.1852	−	50.5503i	0.962208	−	1.66659i
$921$	44.9790	+	11.2106i	1.48211	+	0.369401i
$922$	3.49756			0.115186
$923$	22.5790	−	50.5474i	0.743197	−	1.66379i
$924$	−21.6124	+	3.99975i	−0.710996	+	0.131582i
$925$	1.80886	+	1.04435i	0.0594749	+	0.0343379i
$926$	0.532897	−	0.923005i	0.0175121	−	0.0303318i
$927$	−49.8315	−	26.4853i	−1.63668	−	0.869891i
$928$		−	38.9146i		−	1.27743i
$929$	−11.4306	−	19.7984i	−0.375027	−	0.649565i	0.615304	−	0.788290i	$-0.289033\pi$
$929$	−11.4306	−	19.7984i	−0.375027	−	0.649565i	−0.990331	+	0.138724i	$0.955700\pi$
$930$	20.3610	−	21.0879i	0.667663	−	0.691500i
$931$	−3.42520			−0.112256
$932$	9.53623	+	16.5172i	0.312370	+	0.541040i
$933$	0.183118	−	0.734705i	0.00599500	−	0.0240531i
$934$	3.07485	−	5.32580i	0.100612	−	0.174265i
$935$	0.713566	−	7.38390i	0.0233361	−	0.241479i
$936$	29.3779	−	4.09726i	0.960248	−	0.133923i
$937$			32.3201i			1.05585i	0.849291	+	0.527925i	$0.177030\pi$
$937$			32.3201i			1.05585i	−0.849291	+	0.527925i	$0.822970\pi$
$938$	6.15431	−	10.6596i	0.200945	−	0.348047i
$939$	23.5716	+	5.87499i	0.769231	+	0.191723i
$940$	−14.7494	−	25.5467i	−0.481073	−	0.833243i
$941$		−	8.07497i		−	0.263237i	−0.991300	−	0.131618i	$-0.957983\pi$
$941$		−	8.07497i		−	0.263237i	0.991300	−	0.131618i	$-0.0420173\pi$
$942$	8.78834	+	8.48539i	0.286340	+	0.276469i
$943$	−9.96294	−	17.2563i	−0.324438	−	0.561943i
$944$	0.0886142			0.00288415
$945$	11.3225	−	53.3333i	0.368320	−	1.73493i
$946$	−20.8231	−	14.8638i	−0.677016	−	0.483264i
$947$	−13.4187	+	23.2418i	−0.436048	+	0.755257i	−0.997381	−	0.0723334i	$-0.976955\pi$
$947$	−13.4187	+	23.2418i	−0.436048	+	0.755257i	0.561333	+	0.827590i	$0.310289\pi$
$948$	0.693324	−	0.198870i	0.0225181	−	0.00645899i
$949$	28.0211	+	38.6668i	0.909605	+	1.25518i
$950$		−	15.6741i		−	0.508536i
$951$	−2.22301	−	0.554063i	−0.0720861	−	0.0179667i
$952$	−4.27815	−	2.46999i	−0.138656	−	0.0800529i
$953$	19.3102	+	33.4463i	0.625519	+	1.08343i	0.988440	+	0.151611i	$0.0484460\pi$
$953$	19.3102	+	33.4463i	0.625519	+	1.08343i	−0.362921	+	0.931820i	$0.618221\pi$
$954$	1.49951	−	0.937342i	0.0485483	−	0.0303476i
$955$	−13.8173	+	7.97743i	−0.447118	+	0.258144i
$956$	−0.575100	+	0.332034i	−0.0186001	+	0.0107388i
$957$	37.9902	−	7.03075i	1.22805	−	0.227272i
$958$	3.48182	+	6.03069i	0.112492	+	0.194843i
$959$	2.31297	−	4.00618i	0.0746896	−	0.129366i
$960$	−24.6014	−	6.13164i	−0.794006	−	0.197898i
$961$	−1.14954			−0.0370820
$962$	−0.316377	+	0.708270i	−0.0102004	+	0.0228355i
$963$	−24.2882	+	15.1826i	−0.782677	+	0.489252i
$964$	12.0875	−	20.9361i	0.389312	−	0.674307i
$965$	0.447316	−	0.774774i	0.0143996	−	0.0249409i
$966$	17.0552	−	17.6641i	0.548742	−	0.568334i
$967$	55.0591			1.77058			0.885291	−	0.465038i	$-0.153959\pi$
$967$	55.0591			1.77058			0.885291	+	0.465038i	$0.153959\pi$
$968$	−28.5284	+	9.80105i	−0.916938	+	0.315018i
$969$	−1.76016	+	1.82300i	−0.0565446	+	0.0585633i
$970$	44.0531			1.41446
$971$	24.8428	−	14.3430i	0.797242	−	0.460288i	−0.0452637	−	0.998975i	$-0.514413\pi$
$971$	24.8428	−	14.3430i	0.797242	−	0.460288i	0.842506	+	0.538687i	$0.181079\pi$
$972$	−13.1816	+	15.7224i	−0.422798	+	0.504297i
$973$	−18.1425	−	10.4746i	−0.581622	−	0.335800i
$974$	−4.43617			−0.142144
$975$	18.7284	+	46.5065i	0.599789	+	1.48940i
$976$			3.38879i			0.108473i
$977$	27.3007	−	47.2861i	0.873425	−	1.51282i	0.0149944	−	0.999888i	$-0.495227\pi$
$977$	27.3007	−	47.2861i	0.873425	−	1.51282i	0.858431	−	0.512929i	$-0.171440\pi$
$978$	−18.3437	−	4.57198i	−0.586567	−	0.146196i
$979$	31.9733	−	14.5577i	1.02187	−	0.465267i
$980$	−6.89201			−0.220157
$981$	17.6614	+	9.38698i	0.563886	+	0.299703i
$982$	24.5854	−	14.1944i	0.784552	−	0.452961i
$983$	13.2851			0.423730			0.211865	−	0.977299i	$-0.432046\pi$
$983$	13.2851			0.423730			0.211865	+	0.977299i	$0.432046\pi$
$984$	−11.1477	+	11.5457i	−0.355374	+	0.368062i
$985$	11.5620	+	6.67534i	0.368397	+	0.212694i
$986$	2.98469	+	1.72321i	0.0950520	+	0.0548783i
$987$	−8.62035	−	30.0533i	−0.274389	−	0.956607i
$988$	−11.1441	+	1.15756i	−0.354540	+	0.0368268i
$989$	−55.0090			−1.74919
$990$	1.81838	−	29.6428i	0.0577918	−	0.942109i
$991$	−12.9944	+	22.5070i	−0.412782	+	0.714959i	−0.995193	−	0.0979356i	$-0.968776\pi$
$991$	−12.9944	+	22.5070i	−0.412782	+	0.714959i	0.582411	+	0.812894i	$0.302109\pi$
$992$	16.4037	+	28.4121i	0.520818	+	0.902084i
$993$	37.3767	−	10.7209i	1.18611	−	0.340219i
$994$	−31.9658	+	18.4555i	−1.01389	+	0.585372i
$995$	−7.76950	−	13.4572i	−0.246310	−	0.426621i
$996$	34.2495	−	9.82395i	1.08524	−	0.311284i
$997$	−28.2165	+	16.2908i	−0.893625	+	0.515935i	−0.875126	−	0.483894i	$-0.839222\pi$
$997$	−28.2165	+	16.2908i	−0.893625	+	0.515935i	−0.0184985	+	0.999829i	$0.505889\pi$
$998$	3.87799	−	6.71688i	0.122756	−	0.212619i
$999$	−0.418076	−	1.28562i	−0.0132273	−	0.0406751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.t.a.329.19	yes	104
3.2	odd	2	inner	429.2.t.a.329.34	yes	104
11.10	odd	2	inner	429.2.t.a.329.33	yes	104
13.10	even	6	inner	429.2.t.a.296.20	yes	104
33.32	even	2	inner	429.2.t.a.329.20	yes	104
39.23	odd	6	inner	429.2.t.a.296.33	yes	104
143.10	odd	6	inner	429.2.t.a.296.34	yes	104
429.296	even	6	inner	429.2.t.a.296.19	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.t.a.296.19	✓	104	429.296	even	6	inner
429.2.t.a.296.20	yes	104	13.10	even	6	inner
429.2.t.a.296.33	yes	104	39.23	odd	6	inner
429.2.t.a.296.34	yes	104	143.10	odd	6	inner
429.2.t.a.329.19	yes	104	1.1	even	1	trivial
429.2.t.a.329.20	yes	104	33.32	even	2	inner
429.2.t.a.329.33	yes	104	11.10	odd	2	inner
429.2.t.a.329.34	yes	104	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.716153 - 0.413471i) q^{2} +(-1.68064 - 0.418881i) q^{3} +(-0.658083 - 1.13983i) q^{4} -3.60945 q^{5} +(1.03040 + 0.994878i) q^{6} +(-1.45351 - 2.51755i) q^{7} +2.74228i q^{8} +(2.64908 + 1.40797i) q^{9} +O(q^{10})\)	\(q+(-0.716153 - 0.413471i) q^{2} +(-1.68064 - 0.418881i) q^{3} +(-0.658083 - 1.13983i) q^{4} -3.60945 q^{5} +(1.03040 + 0.994878i) q^{6} +(-1.45351 - 2.51755i) q^{7} +2.74228i q^{8} +(2.64908 + 1.40797i) q^{9} +(2.58492 + 1.49241i) q^{10} +(-2.69945 - 1.92691i) q^{11} +(0.628544 + 2.19131i) q^{12} +(-2.11573 - 2.91953i) q^{13} +2.40394i q^{14} +(6.06618 + 1.51193i) q^{15} +(-0.182314 + 0.315778i) q^{16} +(-0.309839 - 0.536657i) q^{17} +(-1.31499 - 2.10364i) q^{18} +(1.18049 + 2.04467i) q^{19} +(2.37532 + 4.11418i) q^{20} +(1.38826 + 4.83994i) q^{21} +(1.13650 + 2.49610i) q^{22} +(5.10705 + 2.94856i) q^{23} +(1.14869 - 4.60877i) q^{24} +8.02816 q^{25} +(0.308046 + 2.96563i) q^{26} +(-3.86236 - 3.47594i) q^{27} +(-1.91306 + 3.31352i) q^{28} +(3.36278 - 5.82450i) q^{29} +(-3.71917 - 3.59097i) q^{30} +5.67006i q^{31} +(5.01089 - 2.89304i) q^{32} +(3.72965 + 4.36918i) q^{33} +0.512438i q^{34} +(5.24637 + 9.08699i) q^{35} +(-0.138456 - 3.94607i) q^{36} +(0.225314 + 0.130085i) q^{37} -1.95239i q^{38} +(2.33284 + 5.79291i) q^{39} -9.89813i q^{40} +(-2.92623 - 1.68946i) q^{41} +(1.00696 - 4.04014i) q^{42} +(-8.07839 + 4.66406i) q^{43} +(-0.419892 + 4.34499i) q^{44} +(-9.56172 - 5.08202i) q^{45} +(-2.43829 - 4.22324i) q^{46} -6.20944 q^{47} +(0.438677 - 0.454339i) q^{48} +(-0.725377 + 1.25639i) q^{49} +(-5.74939 - 3.31941i) q^{50} +(0.295931 + 1.03171i) q^{51} +(-1.93545 + 4.33288i) q^{52} +0.712815i q^{53} +(1.32884 + 4.08628i) q^{54} +(9.74354 + 6.95509i) q^{55} +(6.90383 - 3.98593i) q^{56} +(-1.12750 - 3.93083i) q^{57} +(-4.81652 + 2.78082i) q^{58} +(-0.121513 - 0.210467i) q^{59} +(-2.26870 - 7.90942i) q^{60} +(8.04868 - 4.64691i) q^{61} +(2.34440 - 4.06063i) q^{62} +(-0.305808 - 8.71569i) q^{63} -4.05550 q^{64} +(7.63664 + 10.5379i) q^{65} +(-0.864468 - 4.67110i) q^{66} +(-4.43422 - 2.56010i) q^{67} +(-0.407800 + 0.706330i) q^{68} +(-7.34800 - 7.09470i) q^{69} -8.67690i q^{70} +(7.67720 + 13.2973i) q^{71} +(-3.86106 + 7.26450i) q^{72} -13.2442 q^{73} +(-0.107573 - 0.186322i) q^{74} +(-13.4924 - 3.36285i) q^{75} +(1.55372 - 2.69112i) q^{76} +(-0.927415 + 9.59678i) q^{77} +(0.724533 - 5.11317i) q^{78} -0.316398i q^{79} +(0.658055 - 1.13979i) q^{80} +(5.03521 + 7.45967i) q^{81} +(1.39709 + 2.41982i) q^{82} -15.6297i q^{83} +(4.60313 - 4.76747i) q^{84} +(1.11835 + 1.93704i) q^{85} +7.71382 q^{86} +(-8.09138 + 8.38026i) q^{87} +(5.28412 - 7.40264i) q^{88} +(-5.29627 + 9.17341i) q^{89} +(4.74639 + 7.59300i) q^{90} +(-4.27484 + 9.57003i) q^{91} -7.76159i q^{92} +(2.37508 - 9.52930i) q^{93} +(4.44691 + 2.56742i) q^{94} +(-4.26092 - 7.38013i) q^{95} +(-9.63333 + 2.76318i) q^{96} +(12.7818 - 7.37955i) q^{97} +(1.03896 - 0.599844i) q^{98} +(-4.43801 - 8.90528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9}+O(q^{10}) \) 104 * q - 2 * q^3 + 44 * q^4 - 6 * q^9	\( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9} - 4 q^{12} - 36 q^{15} - 44 q^{16} - 12 q^{22} + 64 q^{25} + 4 q^{27} + 12 q^{33} + 28 q^{36} - 12 q^{37} + 50 q^{42} - 66 q^{45} + 16 q^{48} - 24 q^{49} - 8 q^{55} - 24 q^{58} - 104 q^{64} - 60 q^{66} - 60 q^{67} - 42 q^{69} - 42 q^{75} + 16 q^{78} - 22 q^{81} - 16 q^{82} + 92 q^{88} - 84 q^{91} + 126 q^{93} + 36 q^{97}+O(q^{100}) \) 104 * q - 2 * q^3 + 44 * q^4 - 6 * q^9 - 4 * q^12 - 36 * q^15 - 44 * q^16 - 12 * q^22 + 64 * q^25 + 4 * q^27 + 12 * q^33 + 28 * q^36 - 12 * q^37 + 50 * q^42 - 66 * q^45 + 16 * q^48 - 24 * q^49 - 8 * q^55 - 24 * q^58 - 104 * q^64 - 60 * q^66 - 60 * q^67 - 42 * q^69 - 42 * q^75 + 16 * q^78 - 22 * q^81 - 16 * q^82 + 92 * q^88 - 84 * q^91 + 126 * q^93 + 36 * q^97

Introduction

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