LMFDB - Embedded newform 273.2.n.c.8.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(8,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("273.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.7
Character	$\chi$	$=$	273.8
Dual form			273.2.n.c.239.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08486 + 1.08486i) q^{2} +(1.14443 + 1.30011i) q^{3} -0.353851i q^{4} +(-0.879295 + 0.879295i) q^{5} +(-2.65199 - 0.168890i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.78584 - 1.78584i) q^{8} +(-0.380562 + 2.97576i) q^{9} +O(q^{10})$	\(q+(-1.08486 + 1.08486i) q^{2} +(1.14443 + 1.30011i) q^{3} -0.353851i q^{4} +(-0.879295 + 0.879295i) q^{5} +(-2.65199 - 0.168890i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.78584 - 1.78584i) q^{8} +(-0.380562 + 2.97576i) q^{9} -1.90783i q^{10} +(-0.135065 - 0.135065i) q^{11} +(0.460044 - 0.404957i) q^{12} +(-3.31468 + 1.41876i) q^{13} -1.53423i q^{14} +(-2.14947 - 0.136887i) q^{15} +4.58249 q^{16} +3.19446 q^{17} +(-2.81544 - 3.64115i) q^{18} +(-0.0287763 - 0.0287763i) q^{19} +(0.311139 + 0.311139i) q^{20} +(-1.72855 - 0.110081i) q^{21} +0.293054 q^{22} +1.05877 q^{23} +(0.278018 - 4.36556i) q^{24} +3.45368i q^{25} +(2.05681 - 5.13513i) q^{26} +(-4.30434 + 2.91078i) q^{27} +(0.250210 + 0.250210i) q^{28} -2.50919i q^{29} +(2.48038 - 2.18337i) q^{30} +(0.0596109 + 0.0596109i) q^{31} +(-1.39968 + 1.39968i) q^{32} +(0.0210267 - 0.330172i) q^{33} +(-3.46554 + 3.46554i) q^{34} -1.24351i q^{35} +(1.05298 + 0.134662i) q^{36} +(1.80281 - 1.80281i) q^{37} +0.0624367 q^{38} +(-5.63796 - 2.68577i) q^{39} +3.14057 q^{40} +(-3.83398 + 3.83398i) q^{41} +(1.99466 - 1.75581i) q^{42} +4.62074i q^{43} +(-0.0477930 + 0.0477930i) q^{44} +(-2.28195 - 2.95120i) q^{45} +(-1.14862 + 1.14862i) q^{46} +(-1.94994 - 1.94994i) q^{47} +(5.24434 + 5.95773i) q^{48} -1.00000i q^{49} +(-3.74677 - 3.74677i) q^{50} +(3.65583 + 4.15314i) q^{51} +(0.502030 + 1.17290i) q^{52} +3.75424i q^{53} +(1.51182 - 7.82741i) q^{54} +0.237524 q^{55} +2.52557 q^{56} +(0.00447986 - 0.0703448i) q^{57} +(2.72213 + 2.72213i) q^{58} +(10.5526 + 10.5526i) q^{59} +(-0.0484377 + 0.760592i) q^{60} +12.0856 q^{61} -0.129339 q^{62} +(-1.83509 - 2.37328i) q^{63} +6.12806i q^{64} +(1.66708 - 4.16209i) q^{65} +(0.335380 + 0.381002i) q^{66} +(6.24374 + 6.24374i) q^{67} -1.13036i q^{68} +(1.21169 + 1.37652i) q^{69} +(1.34904 + 1.34904i) q^{70} +(7.33792 - 7.33792i) q^{71} +(5.99388 - 4.63463i) q^{72} +(0.460100 - 0.460100i) q^{73} +3.91161i q^{74} +(-4.49016 + 3.95249i) q^{75} +(-0.0101825 + 0.0101825i) q^{76} +0.191011 q^{77} +(9.03010 - 3.20272i) q^{78} +6.30427 q^{79} +(-4.02936 + 4.02936i) q^{80} +(-8.71035 - 2.26493i) q^{81} -8.31867i q^{82} +(-7.87129 + 7.87129i) q^{83} +(-0.0389524 + 0.611649i) q^{84} +(-2.80887 + 2.80887i) q^{85} +(-5.01287 - 5.01287i) q^{86} +(3.26222 - 2.87159i) q^{87} +0.482411i q^{88} +(8.78228 + 8.78228i) q^{89} +(5.67725 + 0.726047i) q^{90} +(1.34062 - 3.34705i) q^{91} -0.374648i q^{92} +(-0.00928013 + 0.145721i) q^{93} +4.23083 q^{94} +0.0506058 q^{95} +(-3.42157 - 0.217900i) q^{96} +(-13.0347 - 13.0347i) q^{97} +(1.08486 + 1.08486i) q^{98} +(0.453323 - 0.350522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) $ 48 * q + 8 * q^3 + 4 * q^6	$ 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) $ 48 * q + 8 * q^3 + 4 * q^6 + 8 * q^13 - 16 * q^15 - 72 * q^16 - 12 * q^18 + 40 * q^19 + 16 * q^22 + 8 * q^24 - 16 * q^27 + 44 * q^33 - 32 * q^34 - 8 * q^37 - 4 * q^39 - 48 * q^40 - 8 * q^42 + 44 * q^45 - 32 * q^46 + 80 * q^48 - 72 * q^52 + 44 * q^54 - 80 * q^55 - 52 * q^57 + 16 * q^58 + 44 * q^60 - 64 * q^61 + 24 * q^63 - 152 * q^66 + 56 * q^67 + 16 * q^70 + 16 * q^72 + 32 * q^73 + 104 * q^76 - 44 * q^78 + 8 * q^79 + 12 * q^84 - 96 * q^85 - 72 * q^87 - 8 * q^91 - 8 * q^93 + 160 * q^94 + 8 * q^96 - 32 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.08486	+	1.08486i	−0.767113	+	0.767113i	−0.977597	−	0.210484i	$-0.932496\pi$
$2$	−1.08486	+	1.08486i	−0.767113	+	0.767113i	0.210484	+	0.977597i	$0.432496\pi$
$3$	1.14443	+	1.30011i	0.660737	+	0.750618i
$3$	1.14443	+	1.30011i	0.660737	+	0.750618i
$4$		−	0.353851i		−	0.176925i
$5$	−0.879295	+	0.879295i	−0.393233	+	0.393233i	−0.875838	−	0.482605i	$-0.839691\pi$
$5$	−0.879295	+	0.879295i	−0.393233	+	0.393233i	0.482605	+	0.875838i	$0.339691\pi$
$6$	−2.65199	−	0.168890i	−1.08267	−	0.0689489i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−1.78584	−	1.78584i	−0.631391	−	0.631391i
$9$	−0.380562	+	2.97576i	−0.126854	+	0.991921i
$10$		−	1.90783i		−	0.603308i
$11$	−0.135065	−	0.135065i	−0.0407237	−	0.0407237i	0.686452	−	0.727175i	$-0.259167\pi$
$11$	−0.135065	−	0.135065i	−0.0407237	−	0.0407237i	−0.727175	+	0.686452i	$0.759167\pi$
$12$	0.460044	−	0.404957i	0.132803	−	0.116901i
$13$	−3.31468	+	1.41876i	−0.919327	+	0.393493i
$13$	−3.31468	+	1.41876i	−0.919327	+	0.393493i
$14$		−	1.53423i		−	0.410039i
$15$	−2.14947	−	0.136887i	−0.554991	−	0.0353442i
$16$	4.58249			1.14562
$17$	3.19446			0.774769			0.387385	−	0.921918i	$-0.373379\pi$
$17$	3.19446			0.774769			0.387385	+	0.921918i	$0.373379\pi$
$18$	−2.81544	−	3.64115i	−0.663605	−	0.858227i
$19$	−0.0287763	−	0.0287763i	−0.00660174	−	0.00660174i	0.703798	−	0.710400i	$-0.251486\pi$
$19$	−0.0287763	−	0.0287763i	−0.00660174	−	0.00660174i	−0.710400	+	0.703798i	$0.751486\pi$
$20$	0.311139	+	0.311139i	0.0695729	+	0.0695729i
$21$	−1.72855	−	0.110081i	−0.377200	−	0.0240217i
$22$	0.293054			0.0624794
$23$	1.05877			0.220770			0.110385	−	0.993889i	$-0.464792\pi$
$23$	1.05877			0.220770			0.110385	+	0.993889i	$0.464792\pi$
$24$	0.278018	−	4.36556i	0.0567501	−	0.891117i
$25$			3.45368i			0.690736i
$26$	2.05681	−	5.13513i	0.403374	−	1.00708i
$27$	−4.30434	+	2.91078i	−0.828371	+	0.560180i
$28$	0.250210	+	0.250210i	0.0472853	+	0.0472853i
$29$		−	2.50919i		−	0.465945i	−0.972483	−	0.232973i	$-0.925155\pi$
$29$		−	2.50919i		−	0.465945i	0.972483	−	0.232973i	$-0.0748452\pi$
$30$	2.48038	−	2.18337i	0.452854	−	0.398628i
$31$	0.0596109	+	0.0596109i	0.0107064	+	0.0107064i	0.712440	−	0.701733i	$-0.247590\pi$
$31$	0.0596109	+	0.0596109i	0.0107064	+	0.0107064i	−0.701733	+	0.712440i	$0.747590\pi$
$32$	−1.39968	+	1.39968i	−0.247431	+	0.247431i
$33$	0.0210267	−	0.330172i	0.00366029	−	0.0574756i
$34$	−3.46554	+	3.46554i	−0.594336	+	0.594336i
$35$		−	1.24351i		−	0.210192i
$36$	1.05298	+	0.134662i	0.175496	+	0.0224437i
$37$	1.80281	−	1.80281i	0.296381	−	0.296381i	−0.543214	−	0.839594i	$-0.682793\pi$
$37$	1.80281	−	1.80281i	0.296381	−	0.296381i	0.839594	+	0.543214i	$0.182793\pi$
$38$	0.0624367			0.0101286
$39$	−5.63796	−	2.68577i	−0.902796	−	0.430068i
$40$	3.14057			0.496568
$41$	−3.83398	+	3.83398i	−0.598767	+	0.598767i	−0.939984	−	0.341218i	$-0.889161\pi$
$41$	−3.83398	+	3.83398i	−0.598767	+	0.598767i	0.341218	+	0.939984i	$0.389161\pi$
$42$	1.99466	−	1.75581i	0.307783	−	0.270928i
$43$			4.62074i			0.704656i	0.935877	+	0.352328i	$0.114610\pi$
$43$			4.62074i			0.704656i	−0.935877	+	0.352328i	$0.885390\pi$
$44$	−0.0477930	+	0.0477930i	−0.00720506	+	0.00720506i
$45$	−2.28195	−	2.95120i	−0.340173	−	0.439939i
$46$	−1.14862	+	1.14862i	−0.169355	+	0.169355i
$47$	−1.94994	−	1.94994i	−0.284428	−	0.284428i	0.550444	−	0.834872i	$-0.314458\pi$
$47$	−1.94994	−	1.94994i	−0.284428	−	0.284428i	−0.834872	+	0.550444i	$0.814458\pi$
$48$	5.24434	+	5.95773i	0.756955	+	0.859925i
$49$		−	1.00000i		−	0.142857i
$50$	−3.74677	−	3.74677i	−0.529873	−	0.529873i
$51$	3.65583	+	4.15314i	0.511919	+	0.581556i
$52$	0.502030	+	1.17290i	0.0696190	+	0.162652i
$53$			3.75424i			0.515685i	0.966187	+	0.257843i	$0.0830116\pi$
$53$			3.75424i			0.515685i	−0.966187	+	0.257843i	$0.916988\pi$
$54$	1.51182	−	7.82741i	0.205733	−	1.06518i
$55$	0.237524			0.0320278
$56$	2.52557			0.337493
$57$	0.00447986	−	0.0703448i	0.000593371	−	0.00931740i
$58$	2.72213	+	2.72213i	0.357433	+	0.357433i
$59$	10.5526	+	10.5526i	1.37384	+	1.37384i	0.854679	+	0.519157i	$0.173754\pi$
$59$	10.5526	+	10.5526i	1.37384	+	1.37384i	0.519157	+	0.854679i	$0.326246\pi$
$60$	−0.0484377	+	0.760592i	−0.00625328	+	0.0981920i
$61$	12.0856			1.54740			0.773699	−	0.633553i	$-0.218404\pi$
$61$	12.0856			1.54740			0.773699	+	0.633553i	$0.218404\pi$
$62$	−0.129339			−0.0164261
$63$	−1.83509	−	2.37328i	−0.231199	−	0.299005i
$64$			6.12806i			0.766008i
$65$	1.66708	−	4.16209i	0.206775	−	0.516244i
$66$	0.335380	+	0.381002i	0.0412824	+	0.0468981i
$67$	6.24374	+	6.24374i	0.762794	+	0.762794i	0.976827	−	0.214032i	$-0.0686598\pi$
$67$	6.24374	+	6.24374i	0.762794	+	0.762794i	−0.214032	+	0.976827i	$0.568660\pi$
$68$		−	1.13036i		−	0.137076i
$69$	1.21169	+	1.37652i	0.145871	+	0.165714i
$70$	1.34904	+	1.34904i	0.161241	+	0.161241i
$71$	7.33792	−	7.33792i	0.870851	−	0.870851i	−0.121714	−	0.992565i	$-0.538839\pi$
$71$	7.33792	−	7.33792i	0.870851	−	0.870851i	0.992565	+	0.121714i	$0.0388391\pi$
$72$	5.99388	−	4.63463i	0.706385	−	0.546196i
$73$	0.460100	−	0.460100i	0.0538506	−	0.0538506i	−0.679669	−	0.733519i	$-0.737876\pi$
$73$	0.460100	−	0.460100i	0.0538506	−	0.0538506i	0.733519	+	0.679669i	$0.237876\pi$
$74$			3.91161i			0.454715i
$75$	−4.49016	+	3.95249i	−0.518479	+	0.456395i
$76$	−0.0101825	+	0.0101825i	−0.00116802	+	0.00116802i
$77$	0.191011			0.0217677
$78$	9.03010	−	3.20272i	1.02246	−	0.362636i
$79$	6.30427			0.709286			0.354643	−	0.935002i	$-0.384602\pi$
$79$	6.30427			0.709286			0.354643	+	0.935002i	$0.384602\pi$
$80$	−4.02936	+	4.02936i	−0.450496	+	0.450496i
$81$	−8.71035	−	2.26493i	−0.967816	−	0.251658i
$82$		−	8.31867i		−	0.918644i
$83$	−7.87129	+	7.87129i	−0.863987	+	0.863987i	−0.991798	−	0.127812i	$-0.959205\pi$
$83$	−7.87129	+	7.87129i	−0.863987	+	0.863987i	0.127812	+	0.991798i	$0.459205\pi$
$84$	−0.0389524	+	0.611649i	−0.00425005	+	0.0667363i
$85$	−2.80887	+	2.80887i	−0.304665	+	0.304665i
$86$	−5.01287	−	5.01287i	−0.540551	−	0.540551i
$87$	3.26222	−	2.87159i	0.349747	−	0.307867i
$88$			0.482411i			0.0514252i
$89$	8.78228	+	8.78228i	0.930920	+	0.930920i	0.997763	−	0.0668438i	$-0.0212929\pi$
$89$	8.78228	+	8.78228i	0.930920	+	0.930920i	−0.0668438	+	0.997763i	$0.521293\pi$
$90$	5.67725	+	0.726047i	0.598434	+	0.0765321i
$91$	1.34062	−	3.34705i	0.140535	−	0.350866i
$92$		−	0.374648i		−	0.0390598i
$93$	−0.00928013	+	0.145721i	−0.000962305	+	0.0151106i
$94$	4.23083			0.436377
$95$	0.0506058			0.00519204
$96$	−3.42157	−	0.217900i	−0.349213	−	0.0222394i
$97$	−13.0347	−	13.0347i	−1.32347	−	1.32347i	−0.910945	−	0.412527i	$-0.864646\pi$
$97$	−13.0347	−	13.0347i	−1.32347	−	1.32347i	−0.412527	−	0.910945i	$-0.635354\pi$
$98$	1.08486	+	1.08486i	0.109588	+	0.109588i
$99$	0.453323	−	0.350522i	0.0455607	−	0.0352287i
$100$	1.22209			0.122209
$101$	5.88163			0.585244			0.292622	−	0.956228i	$-0.405472\pi$
$101$	5.88163			0.585244			0.292622	+	0.956228i	$0.405472\pi$
$102$	−8.47165	−	0.539511i	−0.838819	−	0.0534195i
$103$			16.8620i			1.66146i	0.556673	+	0.830732i	$0.312078\pi$
$103$			16.8620i			1.66146i	−0.556673	+	0.830732i	$0.687922\pi$
$104$	8.45319	+	3.38582i	0.828904	+	0.332007i
$105$	1.61670	−	1.42311i	0.157774	−	0.138881i
$106$	−4.07284	−	4.07284i	−0.395589	−	0.395589i
$107$		−	16.4075i		−	1.58618i	−0.609107	−	0.793088i	$-0.708472\pi$
$107$		−	16.4075i		−	1.58618i	0.609107	−	0.793088i	$-0.291528\pi$
$108$	1.02998	+	1.52310i	0.0991101	+	0.146560i
$109$	−11.4665	−	11.4665i	−1.09829	−	1.09829i	−0.994610	−	0.103684i	$-0.966937\pi$
$109$	−11.4665	−	11.4665i	−1.09829	−	1.09829i	−0.103684	−	0.994610i	$-0.533063\pi$
$110$	−0.257681	+	0.257681i	−0.0245689	+	0.0245689i
$111$	4.40704	+	0.280659i	0.418298	+	0.0266390i
$112$	−3.24031	+	3.24031i	−0.306181	+	0.306181i
$113$			2.82075i			0.265354i	0.991159	+	0.132677i	$0.0423572\pi$
$113$			2.82075i			0.265354i	−0.991159	+	0.132677i	$0.957643\pi$
$114$	0.0714544	+	0.0811744i	0.00669232	+	0.00760268i
$115$	−0.930975	+	0.930975i	−0.0868139	+	0.0868139i
$116$	−0.887880			−0.0824376
$117$	−2.96045	−	10.4036i	−0.273694	−	0.961817i
$118$	−22.8963			−2.10778
$119$	−2.25882	+	2.25882i	−0.207066	+	0.207066i
$120$	3.59416	+	4.08308i	0.328100	+	0.372732i
$121$		−	10.9635i		−	0.996683i
$122$	−13.1112	+	13.1112i	−1.18703	+	1.18703i
$123$	−9.37230	−	0.596868i	−0.845072	−	0.0538178i
$124$	0.0210934	−	0.0210934i	0.00189424	−	0.00189424i
$125$	−7.43328	−	7.43328i	−0.664853	−	0.664853i
$126$	4.56550	+	0.583868i	0.406727	+	0.0520151i
$127$		−	11.2607i		−	0.999230i	−0.866248	−	0.499615i	$-0.833475\pi$
$127$		−	11.2607i		−	0.999230i	0.866248	−	0.499615i	$-0.166525\pi$
$128$	−9.44746	−	9.44746i	−0.835046	−	0.835046i
$129$	−6.00746	+	5.28811i	−0.528928	+	0.465592i
$130$	2.70675	+	6.32384i	0.237398	+	0.554638i
$131$			7.16133i			0.625688i	0.949804	+	0.312844i	$0.101282\pi$
$131$			7.16133i			0.625688i	−0.949804	+	0.312844i	$0.898718\pi$
$132$	−0.116832	−	0.00744034i	−0.0101689	−	0.000647598i
$133$	0.0406959			0.00352878
$134$	−13.5472			−1.17030
$135$	1.22535	−	6.34422i	0.105461	−	0.546024i
$136$	−5.70480	−	5.70480i	−0.489183	−	0.489183i
$137$	8.75820	+	8.75820i	0.748264	+	0.748264i	0.974153	−	0.225889i	$-0.0725287\pi$
$137$	8.75820	+	8.75820i	0.748264	+	0.748264i	−0.225889	+	0.974153i	$0.572529\pi$
$138$	−2.80785	−	0.178816i	−0.239020	−	0.0152218i
$139$	2.47169			0.209646			0.104823	−	0.994491i	$-0.466572\pi$
$139$	2.47169			0.209646			0.104823	+	0.994491i	$0.466572\pi$
$140$	−0.440018			−0.0371883
$141$	0.303564	−	4.76671i	0.0255647	−	0.401429i
$142$			15.9213i			1.33608i
$143$	0.639323	+	0.256073i	0.0534629	+	0.0214139i
$144$	−1.74392	+	13.6364i	−0.145327	+	1.13637i
$145$	2.20632	+	2.20632i	0.183225	+	0.183225i
$146$			0.998289i			0.0826190i
$147$	1.30011	−	1.14443i	0.107231	−	0.0943910i
$148$	−0.637927	−	0.637927i	−0.0524373	−	0.0524373i
$149$	−3.16790	+	3.16790i	−0.259524	+	0.259524i	−0.824861	−	0.565336i	$-0.808746\pi$
$149$	−3.16790	+	3.16790i	−0.259524	+	0.259524i	0.565336	+	0.824861i	$0.308746\pi$
$150$	0.583291	−	9.15911i	0.0476255	−	0.747838i
$151$	13.4162	−	13.4162i	1.09179	−	1.09179i	0.0964575	−	0.995337i	$-0.469249\pi$
$151$	13.4162	−	13.4162i	1.09179	−	1.09179i	0.995337	−	0.0964575i	$-0.0307512\pi$
$152$			0.102780i			0.00833657i
$153$	−1.21569	+	9.50595i	−0.0982826	+	0.768510i
$154$	−0.207221	+	0.207221i	−0.0166983	+	0.0166983i
$155$	−0.104831			−0.00842024
$156$	−0.950364	+	1.99500i	−0.0760900	+	0.159728i
$157$	−18.6432			−1.48789			−0.743943	−	0.668243i	$-0.767047\pi$
$157$	−18.6432			−1.48789			−0.743943	+	0.668243i	$0.767047\pi$
$158$	−6.83927	+	6.83927i	−0.544103	+	0.544103i
$159$	−4.88092	+	4.29647i	−0.387082	+	0.340732i
$160$		−	2.46147i		−	0.194596i
$161$	−0.748666	+	0.748666i	−0.0590032	+	0.0590032i
$162$	11.9067	−	6.99239i	0.935475	−	0.549374i
$163$	−4.47387	+	4.47387i	−0.350421	+	0.350421i	−0.860266	−	0.509845i	$-0.829703\pi$
$163$	−4.47387	+	4.47387i	−0.350421	+	0.350421i	0.509845	+	0.860266i	$0.329703\pi$
$164$	1.35666	+	1.35666i	0.105937	+	0.105937i
$165$	0.271830	+	0.308807i	0.0211619	+	0.0240406i
$166$		−	17.0785i		−	1.32555i
$167$	2.27059	+	2.27059i	0.175703	+	0.175703i	0.789480	−	0.613776i	$-0.210350\pi$
$167$	2.27059	+	2.27059i	0.175703	+	0.175703i	−0.613776	+	0.789480i	$0.710350\pi$
$168$	2.89033	+	3.28351i	0.222994	+	0.253328i
$169$	8.97424	−	9.40548i	0.690326	−	0.723498i
$170$		−	6.09447i		−	0.467425i
$171$	0.0965827	−	0.0746804i	0.00738587	−	0.00571095i
$172$	1.63505			0.124672
$173$	−19.7250			−1.49967			−0.749833	−	0.661627i	$-0.769866\pi$
$173$	−19.7250			−1.49967			−0.749833	+	0.661627i	$0.769866\pi$
$174$	−0.423777	+	6.65434i	−0.0321264	+	0.504464i
$175$	−2.44212	−	2.44212i	−0.184607	−	0.184607i
$176$	−0.618935	−	0.618935i	−0.0466540	−	0.0466540i
$177$	−1.64282	+	25.7963i	−0.123482	+	1.93897i
$178$	−19.0551			−1.42824
$179$	15.1369			1.13139			0.565694	−	0.824615i	$-0.308608\pi$
$179$	15.1369			1.13139			0.565694	+	0.824615i	$0.308608\pi$
$180$	−1.04429	+	0.807470i	−0.0778364	+	0.0601852i
$181$		−	11.7346i		−	0.872227i	−0.899892	−	0.436114i	$-0.856355\pi$
$181$		−	11.7346i		−	0.872227i	0.899892	−	0.436114i	$-0.143645\pi$
$182$	2.17670	+	5.08547i	0.161348	+	0.376960i
$183$	13.8311	+	15.7125i	1.02242	+	1.16150i
$184$	−1.89081	−	1.89081i	−0.139392	−	0.139392i
$185$			3.17041i			0.233093i
$186$	−0.148019	−	0.168155i	−0.0108533	−	0.0123297i
$187$	−0.431460	−	0.431460i	−0.0315515	−	0.0315515i
$188$	−0.689989	+	0.689989i	−0.0503226	+	0.0503226i
$189$	0.985396	−	5.10186i	0.0716770	−	0.371106i
$190$	−0.0549003	+	0.0549003i	−0.00398289	+	0.00398289i
$191$		−	22.6999i		−	1.64251i	−0.570563	−	0.821254i	$-0.693275\pi$
$191$		−	22.6999i		−	1.64251i	0.570563	−	0.821254i	$-0.306725\pi$
$192$	−7.96714	+	7.01313i	−0.574979	+	0.506129i
$193$	18.2312	−	18.2312i	1.31231	−	1.31231i	0.392596	−	0.919711i	$-0.371577\pi$
$193$	18.2312	−	18.2312i	1.31231	−	1.31231i	0.919711	−	0.392596i	$-0.128423\pi$
$194$	28.2817			2.03051
$195$	7.31902	−	2.59585i	0.524126	−	0.185892i
$196$	−0.353851			−0.0252751
$197$	3.48543	−	3.48543i	0.248327	−	0.248327i	−0.571957	−	0.820284i	$-0.693816\pi$
$197$	3.48543	−	3.48543i	0.248327	−	0.248327i	0.820284	+	0.571957i	$0.193816\pi$
$198$	−0.111525	+	0.872060i	−0.00792576	+	0.0619746i
$199$		−	0.651310i		−	0.0461701i	−0.999734	−	0.0230851i	$-0.992651\pi$
$199$		−	0.651310i		−	0.0461701i	0.999734	−	0.0230851i	$-0.00734886\pi$
$200$	6.16773	−	6.16773i	0.436125	−	0.436125i
$201$	−0.972016	+	15.2631i	−0.0685607	+	1.07657i
$202$	−6.38075	+	6.38075i	−0.448948	+	0.448948i
$203$	1.77427	+	1.77427i	0.124529	+	0.124529i
$204$	1.46959	−	1.29362i	0.102892	−	0.0905714i
$205$		−	6.74240i		−	0.470909i
$206$	−18.2930	−	18.2930i	−1.27453	−	1.27453i
$207$	−0.402929	+	3.15066i	−0.0280055	+	0.218986i
$208$	−15.1895	+	6.50146i	−1.05320	+	0.450795i
$209$			0.00777336i			0.000537695i
$210$	−0.210016	+	3.29777i	−0.0144925	+	0.227568i
$211$	14.7026			1.01217			0.506083	−	0.862485i	$-0.331093\pi$
$211$	14.7026			1.01217			0.506083	+	0.862485i	$0.331093\pi$
$212$	1.32844			0.0912378
$213$	17.9378	+	1.14236i	1.22908	+	0.0782730i
$214$	17.7999	+	17.7999i	1.21678	+	1.21678i
$215$	−4.06300	−	4.06300i	−0.277094	−	0.277094i
$216$	12.8851	+	2.48868i	0.876719	+	0.169333i
$217$	−0.0843025			−0.00572283
$218$	24.8792			1.68503
$219$	1.12473	+	0.0716276i	0.0760023	+	0.00484015i
$220$		−	0.0840482i		−	0.00566653i
$221$	−10.5886	+	4.53217i	−0.712267	+	0.304867i
$222$	−5.08551	+	4.47656i	−0.341317	+	0.300447i
$223$	18.0386	+	18.0386i	1.20795	+	1.20795i	0.971688	+	0.236266i	$0.0759237\pi$
$223$	18.0386	+	18.0386i	1.20795	+	1.20795i	0.236266	+	0.971688i	$0.424076\pi$
$224$		−	1.97945i		−	0.132257i
$225$	−10.2773	−	1.31434i	−0.685156	−	0.0876226i
$226$	−3.06012	−	3.06012i	−0.203556	−	0.203556i
$227$	12.4246	−	12.4246i	0.824653	−	0.824653i	−0.162118	−	0.986771i	$-0.551833\pi$
$227$	12.4246	−	12.4246i	0.824653	−	0.824653i	0.986771	+	0.162118i	$0.0518327\pi$
$228$	−0.0248916	−	0.00158520i	−0.00164849	−	0.000104983i
$229$	−3.40411	+	3.40411i	−0.224950	+	0.224950i	−0.810579	−	0.585629i	$-0.800847\pi$
$229$	−3.40411	+	3.40411i	−0.224950	+	0.224950i	0.585629	+	0.810579i	$0.300847\pi$
$230$		−	2.01996i		−	0.133192i
$231$	0.218599	+	0.248335i	0.0143827	+	0.0163392i
$232$	−4.48103	+	4.48103i	−0.294194	+	0.294194i
$233$	−9.44711			−0.618901			−0.309450	−	0.950916i	$-0.600145\pi$
$233$	−9.44711			−0.618901			−0.309450	+	0.950916i	$0.600145\pi$
$234$	14.4982	+	8.07483i	0.947777	+	0.527868i
$235$	3.42915			0.223693
$236$	3.73406	−	3.73406i	0.243067	−	0.243067i
$237$	7.21480	+	8.19624i	0.468651	+	0.532403i
$238$		−	4.90102i		−	0.317686i
$239$	−6.96107	+	6.96107i	−0.450274	+	0.450274i	−0.895445	−	0.445171i	$-0.853143\pi$
$239$	−6.96107	+	6.96107i	−0.450274	+	0.450274i	0.445171	+	0.895445i	$0.353143\pi$
$240$	−9.84993	−	0.627285i	−0.635810	−	0.0404911i
$241$	−11.8164	+	11.8164i	−0.761159	+	0.761159i	−0.976532	−	0.215373i	$-0.930903\pi$
$241$	−11.8164	+	11.8164i	−0.761159	+	0.761159i	0.215373	+	0.976532i	$0.430903\pi$
$242$	11.8939	+	11.8939i	0.764569	+	0.764569i
$243$	−7.02373	−	13.9164i	−0.450572	−	0.892740i
$244$		−	4.27649i		−	0.273774i
$245$	0.879295	+	0.879295i	0.0561761	+	0.0561761i
$246$	10.8152	−	9.52013i	0.689550	−	0.606982i
$247$	0.136211	+	0.0545577i	0.00866690	+	0.00347142i
$248$		−	0.212911i		−	0.0135199i
$249$	−19.2417	−	1.22539i	−1.21939	−	0.0776560i
$250$	16.1282			1.02003
$251$	−7.20244			−0.454614			−0.227307	−	0.973823i	$-0.572992\pi$
$251$	−7.20244			−0.454614			−0.227307	+	0.973823i	$0.572992\pi$
$252$	−0.839788	+	0.649347i	−0.0529017	+	0.0409050i
$253$	−0.143004	−	0.143004i	−0.00899056	−	0.00899056i
$254$	12.2164	+	12.2164i	0.766522	+	0.766522i
$255$	−6.86639	−	0.437281i	−0.429990	−	0.0273836i
$256$	8.24227			0.515142
$257$	5.03844			0.314289			0.157145	−	0.987576i	$-0.449771\pi$
$257$	5.03844			0.314289			0.157145	+	0.987576i	$0.449771\pi$
$258$	0.780396	−	12.2541i	0.0485853	−	0.762909i
$259$			2.54956i			0.158422i
$260$	−1.47276	−	0.589896i	−0.0913367	−	0.0365838i
$261$	7.46676	+	0.954903i	0.462181	+	0.0591070i
$262$	−7.76906	−	7.76906i	−0.479974	−	0.479974i
$263$		−	29.2688i		−	1.80479i	−0.430907	−	0.902396i	$-0.641806\pi$
$263$		−	29.2688i		−	1.80479i	0.430907	−	0.902396i	$-0.358194\pi$
$264$	−0.627186	+	0.552085i	−0.0386006	+	0.0339785i
$265$	−3.30109	−	3.30109i	−0.202784	−	0.202784i
$266$	−0.0441494	+	0.0441494i	−0.00270697	+	0.00270697i
$267$	−1.36721	+	21.4686i	−0.0836720	+	1.31386i
$268$	2.20935	−	2.20935i	0.134958	−	0.134958i
$269$		−	16.5644i		−	1.00995i	−0.863135	−	0.504974i	$-0.831502\pi$
$269$		−	16.5644i		−	1.00995i	0.863135	−	0.504974i	$-0.168498\pi$
$270$	5.55327	+	8.21194i	0.337961	+	0.499763i
$271$	8.04347	−	8.04347i	0.488606	−	0.488606i	−0.419260	−	0.907866i	$-0.637711\pi$
$271$	8.04347	−	8.04347i	0.488606	−	0.488606i	0.907866	+	0.419260i	$0.137711\pi$
$272$	14.6386			0.887594
$273$	5.88577	−	2.08751i	0.356223	−	0.126342i
$274$	−19.0029			−1.14801
$275$	0.466472	−	0.466472i	0.0281293	−	0.0281293i
$276$	0.487083	−	0.428759i	0.0293190	−	0.0258082i
$277$			23.7775i			1.42865i	0.699813	+	0.714326i	$0.253267\pi$
$277$			23.7775i			1.42865i	−0.699813	+	0.714326i	$0.746733\pi$
$278$	−2.68145	+	2.68145i	−0.160823	+	0.160823i
$279$	−0.200073	+	0.154702i	−0.0119781	+	0.00926178i
$280$	−2.22072	+	2.22072i	−0.132713	+	0.132713i
$281$	−6.72958	−	6.72958i	−0.401453	−	0.401453i	0.477292	−	0.878745i	$-0.341619\pi$
$281$	−6.72958	−	6.72958i	−0.401453	−	0.401453i	−0.878745	+	0.477292i	$0.841619\pi$
$282$	4.84189	+	5.50054i	0.288331	+	0.327553i
$283$			27.5455i			1.63741i	0.574216	+	0.818704i	$0.305307\pi$
$283$			27.5455i			1.63741i	−0.574216	+	0.818704i	$0.694693\pi$
$284$	−2.59653	−	2.59653i	−0.154076	−	0.154076i
$285$	0.0579147	+	0.0657930i	0.00343057	+	0.00389724i
$286$	−0.971382	+	0.415774i	−0.0574390	+	0.0245852i
$287$		−	5.42206i		−	0.320054i
$288$	−3.63246	−	4.69779i	−0.214045	−	0.276820i
$289$	−6.79545			−0.399732
$290$	−4.78711			−0.281108
$291$	2.02922	−	31.8638i	0.118955	−	1.86789i
$292$	−0.162807	−	0.162807i	−0.00952754	−	0.00952754i
$293$	−11.5684	−	11.5684i	−0.675834	−	0.675834i	0.283221	−	0.959055i	$-0.408597\pi$
$293$	−11.5684	−	11.5684i	−0.675834	−	0.675834i	−0.959055	+	0.283221i	$0.908597\pi$
$294$	−0.168890	+	2.65199i	−0.00984985	+	0.154667i
$295$	−18.5578			−1.08047
$296$	−6.43909			−0.374264
$297$	0.974512	+	0.188222i	0.0565469	+	0.0109217i
$298$		−	6.87346i		−	0.398169i
$299$	−3.50950	+	1.50215i	−0.202960	+	0.0868714i
$300$	1.39859	+	1.58885i	0.0807478	+	0.0917321i
$301$	−3.26736	−	3.26736i	−0.188327	−	0.188327i
$302$			29.1094i			1.67506i
$303$	6.73111	+	7.64675i	0.386692	+	0.439294i
$304$	−0.131867	−	0.131867i	−0.00756311	−	0.00756311i
$305$	−10.6268	+	10.6268i	−0.608488	+	0.608488i
$306$	−8.99379	−	11.6315i	−0.514141	−	0.664928i
$307$	0.746212	−	0.746212i	0.0425886	−	0.0425886i	−0.685492	−	0.728080i	$-0.740413\pi$
$307$	0.746212	−	0.746212i	0.0425886	−	0.0425886i	0.728080	+	0.685492i	$0.240413\pi$
$308$		−	0.0675894i		−	0.00385127i
$309$	−21.9224	+	19.2974i	−1.24712	+	1.09779i
$310$	0.113727	−	0.113727i	0.00645927	−	0.00645927i
$311$	13.2027			0.748658			0.374329	−	0.927296i	$-0.377873\pi$
$311$	13.2027			0.748658			0.374329	+	0.927296i	$0.377873\pi$
$312$	5.27215	+	14.8649i	0.298477	+	0.841559i
$313$	12.1325			0.685772			0.342886	−	0.939377i	$-0.388596\pi$
$313$	12.1325			0.685772			0.342886	+	0.939377i	$0.388596\pi$
$314$	20.2253	−	20.2253i	1.14138	−	1.14138i
$315$	3.70040	+	0.473233i	0.208494	+	0.0266637i
$316$		−	2.23077i		−	0.125491i
$317$	−22.4757	+	22.4757i	−1.26236	+	1.26236i	−0.312419	+	0.949945i	$0.601139\pi$
$317$	−22.4757	+	22.4757i	−1.26236	+	1.26236i	−0.949945	+	0.312419i	$0.898861\pi$
$318$	0.634053	−	9.95620i	0.0355559	−	0.558316i
$319$	−0.338904	+	0.338904i	−0.0189750	+	0.0189750i
$320$	−5.38837	−	5.38837i	−0.301219	−	0.301219i
$321$	21.3316	−	18.7773i	1.19061	−	1.04804i
$322$		−	1.62440i		−	0.0905242i
$323$	−0.0919247	−	0.0919247i	−0.00511483	−	0.00511483i
$324$	−0.801446	+	3.08216i	−0.0445248	+	0.171231i
$325$	−4.89994	−	11.4479i	−0.271800	−	0.635013i
$326$		−	9.70707i		−	0.537625i
$327$	1.78509	−	28.0304i	0.0987158	−	1.55008i
$328$	13.6938			0.756112
$329$	2.75763			0.152033
$330$	−0.629911	−	0.0401154i	−0.0346755	−	0.00220828i
$331$	10.1446	+	10.1446i	0.557595	+	0.557595i	0.928622	−	0.371027i	$-0.120994\pi$
$331$	10.1446	+	10.1446i	0.557595	+	0.557595i	−0.371027	+	0.928622i	$0.620994\pi$
$332$	2.78527	+	2.78527i	0.152861	+	0.152861i
$333$	4.67866	+	6.05083i	0.256389	+	0.331583i
$334$	−4.92655			−0.269569
$335$	−10.9802			−0.599911
$336$	−7.92106	−	0.504447i	−0.432129	−	0.0275198i
$337$		−	17.0422i		−	0.928349i	−0.885744	−	0.464175i	$-0.846351\pi$
$337$		−	17.0422i		−	0.928349i	0.885744	−	0.464175i	$-0.153649\pi$
$338$	0.467838	+	19.9395i	0.0254470	+	1.08456i
$339$	−3.66728	+	3.22815i	−0.199179	+	0.175329i
$340$	0.993921	+	0.993921i	0.0539030	+	0.0539030i
$341$		−	0.0161027i		−	0.000872010i
$342$	−0.0237610	+	0.185797i	−0.00128485	+	0.0100467i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	8.25192	−	8.25192i	0.444914	−	0.444914i
$345$	−2.27580	−	0.144933i	−0.122525	−	0.00780292i
$346$	21.3989	−	21.3989i	1.15041	−	1.15041i
$347$		−	22.8998i		−	1.22932i	−0.788791	−	0.614662i	$-0.789292\pi$
$347$		−	22.8998i		−	1.22932i	0.788791	−	0.614662i	$-0.210708\pi$
$348$	−1.01612	−	1.15434i	−0.0544695	−	0.0618791i
$349$	−2.12018	+	2.12018i	−0.113491	+	0.113491i	−0.761572	−	0.648081i	$-0.775572\pi$
$349$	−2.12018	+	2.12018i	−0.113491	+	0.113491i	0.648081	+	0.761572i	$0.275572\pi$
$350$	5.29873			0.283229
$351$	10.1378	−	15.7551i	0.541117	−	0.840947i
$352$	0.378097			0.0201526
$353$	−3.69400	+	3.69400i	−0.196612	+	0.196612i	−0.798546	−	0.601934i	$-0.794397\pi$
$353$	−3.69400	+	3.69400i	−0.196612	+	0.196612i	0.601934	+	0.798546i	$0.294397\pi$
$354$	−26.2032	−	29.7677i	−1.39268	−	1.58213i
$355$			12.9044i			0.684894i
$356$	3.10762	−	3.10762i	0.164703	−	0.164703i
$357$	−5.52177	−	0.351650i	−0.292243	−	0.0186113i
$358$	−16.4215	+	16.4215i	−0.867903	+	0.867903i
$359$	21.5382	+	21.5382i	1.13674	+	1.13674i	0.989030	+	0.147714i	$0.0471915\pi$
$359$	21.5382	+	21.5382i	1.13674	+	1.13674i	0.147714	+	0.989030i	$0.452809\pi$
$360$	−1.19518	+	9.34559i	−0.0629916	+	0.492556i
$361$		−	18.9983i		−	0.999913i
$362$	12.7304	+	12.7304i	0.669097	+	0.669097i
$363$	14.2538	−	12.5470i	0.748128	−	0.658545i
$364$	−1.18436	−	0.474379i	−0.0620772	−	0.0248642i
$365$			0.809127i			0.0423516i
$366$	−32.0507	−	2.04113i	−1.67532	−	0.106691i
$367$	16.1086			0.840860			0.420430	−	0.907325i	$-0.361879\pi$
$367$	16.1086			0.840860			0.420430	+	0.907325i	$0.361879\pi$
$368$	4.85182			0.252919
$369$	−9.94995	−	12.8681i	−0.517974	−	0.669885i
$370$	−3.43946	−	3.43946i	−0.178809	−	0.178809i
$371$	−2.65465	−	2.65465i	−0.137823	−	0.137823i
$372$	0.0515635	+	0.00328378i	0.00267344	+	0.000170256i
$373$	−12.0774			−0.625345			−0.312673	−	0.949861i	$-0.601224\pi$
$373$	−12.0774			−0.625345			−0.312673	+	0.949861i	$0.601224\pi$
$374$	0.936149			0.0484071
$375$	1.15720	−	18.1709i	0.0597577	−	0.938343i
$376$			6.96458i			0.359171i
$377$	3.55994	+	8.31717i	0.183346	+	0.428356i
$378$	4.46580	+	6.60383i	0.229696	+	0.339665i
$379$	−3.23956	−	3.23956i	−0.166405	−	0.166405i	0.618992	−	0.785397i	$-0.287541\pi$
$379$	−3.23956	−	3.23956i	−0.166405	−	0.166405i	−0.785397	+	0.618992i	$0.787541\pi$
$380$		−	0.0179069i		−	0.000918605i
$381$	14.6402	−	12.8871i	0.750040	−	0.660228i
$382$	24.6263	+	24.6263i	1.25999	+	1.25999i
$383$	−15.0555	+	15.0555i	−0.769302	+	0.769302i	−0.977984	−	0.208682i	$-0.933083\pi$
$383$	−15.0555	+	15.0555i	−0.769302	+	0.769302i	0.208682	+	0.977984i	$0.433083\pi$
$384$	1.47077	−	23.0947i	0.0750548	−	1.17855i
$385$	−0.167955	+	0.167955i	−0.00855978	+	0.00855978i
$386$			39.5566i			2.01338i
$387$	−13.7502	−	1.75848i	−0.698964	−	0.0893885i
$388$	−4.61234	+	4.61234i	−0.234156	+	0.234156i
$389$	−38.4715			−1.95058			−0.975291	−	0.220923i	$-0.929093\pi$
$389$	−38.4715			−1.95058			−0.975291	+	0.220923i	$0.929093\pi$
$390$	−5.12399	+	10.7563i	−0.259464	+	0.544665i
$391$	3.38221			0.171046
$392$	−1.78584	+	1.78584i	−0.0901988	+	0.0901988i
$393$	−9.31051	+	8.19564i	−0.469653	+	0.413415i
$394$			7.56242i			0.380989i
$395$	−5.54332	+	5.54332i	−0.278915	+	0.278915i
$396$	−0.124032	−	0.160409i	−0.00623286	−	0.00806084i
$397$	−0.349281	+	0.349281i	−0.0175299	+	0.0175299i	−0.715817	−	0.698287i	$-0.753946\pi$
$397$	−0.349281	+	0.349281i	−0.0175299	+	0.0175299i	0.698287	+	0.715817i	$0.253946\pi$
$398$	0.706581	+	0.706581i	0.0354177	+	0.0354177i
$399$	0.0465736	+	0.0529090i	0.00233159	+	0.00264876i
$400$			15.8265i			0.791323i
$401$	12.8045	+	12.8045i	0.639424	+	0.639424i	0.950413	−	0.310989i	$-0.100660\pi$
$401$	12.8045	+	12.8045i	0.639424	+	0.639424i	−0.310989	+	0.950413i	$0.600660\pi$
$402$	−15.5038	−	17.6128i	−0.773260	−	0.878447i
$403$	−0.282165	−	0.113018i	−0.0140556	−	0.00562980i
$404$		−	2.08122i		−	0.103545i
$405$	9.65050	−	5.66743i	0.479537	−	0.281617i
$406$	−3.84967			−0.191056
$407$	−0.486995			−0.0241394
$408$	0.888115	−	13.9456i	0.0439682	−	0.690410i
$409$	16.0700	+	16.0700i	0.794612	+	0.794612i	0.982240	−	0.187629i	$-0.0600801\pi$
$409$	16.0700	+	16.0700i	0.794612	+	0.794612i	−0.187629	+	0.982240i	$0.560080\pi$
$410$	7.31457	+	7.31457i	0.361241	+	0.361241i
$411$	−1.36346	+	21.4098i	−0.0672547	+	1.05607i
$412$	5.96664			0.293955
$413$	−14.9237			−0.734346
$414$	−2.98091	−	3.85516i	−0.146504	−	0.189471i
$415$		−	13.8424i		−	0.679496i
$416$	2.65369	−	6.62531i	0.130108	−	0.324833i
$417$	2.82868	+	3.21347i	0.138521	+	0.157364i
$418$	−0.00843302	−	0.00843302i	−0.000412473	−	0.000412473i
$419$			13.8494i			0.676587i	0.941041	+	0.338294i	$0.109850\pi$
$419$			13.8494i			0.676587i	−0.941041	+	0.338294i	$0.890150\pi$
$420$	−0.503569	−	0.572070i	−0.0245717	−	0.0279142i
$421$	0.197909	+	0.197909i	0.00964550	+	0.00964550i	0.711913	−	0.702268i	$-0.247829\pi$
$421$	0.197909	+	0.197909i	0.00964550	+	0.00964550i	−0.702268	+	0.711913i	$0.747829\pi$
$422$	−15.9502	+	15.9502i	−0.776446	+	0.776446i
$423$	6.54464	−	5.06049i	0.318211	−	0.246050i
$424$	6.70450	−	6.70450i	0.325599	−	0.325599i
$425$			11.0326i			0.535161i
$426$	−20.6994	+	18.2208i	−1.00289	+	0.882799i
$427$	−8.54579	+	8.54579i	−0.413560	+	0.413560i
$428$	−5.80582			−0.280635
$429$	0.398738	+	1.12425i	0.0192512	+	0.0542792i
$430$	8.81558			0.425125
$431$	−3.37401	+	3.37401i	−0.162521	+	0.162521i	−0.783682	−	0.621162i	$-0.786661\pi$
$431$	−3.37401	+	3.37401i	−0.162521	+	0.162521i	0.621162	+	0.783682i	$0.286661\pi$
$432$	−19.7246	+	13.3386i	−0.949001	+	0.641755i
$433$		−	3.40036i		−	0.163411i	−0.996657	−	0.0817054i	$-0.973963\pi$
$433$		−	3.40036i		−	0.163411i	0.996657	−	0.0817054i	$-0.0260367\pi$
$434$	0.0914566	−	0.0914566i	0.00439005	−	0.00439005i
$435$	−0.343477	+	5.39343i	−0.0164684	+	0.258595i
$436$	−4.05744	+	4.05744i	−0.194316	+	0.194316i
$437$	−0.0304676	−	0.0304676i	−0.00145746	−	0.00145746i
$438$	−1.29788	+	1.14247i	−0.0620153	+	0.0545894i
$439$		−	7.56505i		−	0.361060i	−0.983569	−	0.180530i	$-0.942219\pi$
$439$		−	7.56505i		−	0.361060i	0.983569	−	0.180530i	$-0.0577813\pi$
$440$	−0.424182	−	0.424182i	−0.0202221	−	0.0202221i
$441$	2.97576	+	0.380562i	0.141703	+	0.0181220i
$442$	6.57040	−	16.4040i	0.312522	−	0.780257i
$443$			26.6466i			1.26602i	0.774145	+	0.633009i	$0.218180\pi$
$443$			26.6466i			1.26602i	−0.774145	+	0.633009i	$0.781820\pi$
$444$	0.0993115	−	1.55944i	0.00471312	−	0.0740076i
$445$	−15.4444			−0.732136
$446$	−39.1388			−1.85328
$447$	−7.74405	−	0.493174i	−0.366281	−	0.0233263i
$448$	−4.33319	−	4.33319i	−0.204724	−	0.204724i
$449$	−7.80356	−	7.80356i	−0.368273	−	0.368273i	0.498574	−	0.866847i	$-0.333857\pi$
$449$	−7.80356	−	7.80356i	−0.368273	−	0.368273i	−0.866847	+	0.498574i	$0.833857\pi$
$450$	12.5754	−	9.72361i	0.592809	−	0.458376i
$451$	1.03567			0.0487680
$452$	0.998124			0.0469478
$453$	32.7964	+	2.08861i	1.54091	+	0.0981316i
$454$			26.9581i			1.26520i
$455$	1.76424	+	4.12184i	0.0827091	+	0.193235i
$456$	−0.133625	+	0.117625i	−0.00625757	+	0.00550828i
$457$	10.7720	+	10.7720i	0.503892	+	0.503892i	0.912645	−	0.408753i	$-0.134036\pi$
$457$	10.7720	+	10.7720i	0.503892	+	0.503892i	−0.408753	+	0.912645i	$0.634036\pi$
$458$		−	7.38597i		−	0.345124i
$459$	−13.7500	+	9.29836i	−0.641796	+	0.434010i
$460$	0.329426	+	0.329426i	0.0153596	+	0.0153596i
$461$	5.57821	−	5.57821i	0.259803	−	0.259803i	−0.565171	−	0.824974i	$-0.691190\pi$
$461$	5.57821	−	5.57821i	0.259803	−	0.259803i	0.824974	+	0.565171i	$0.191190\pi$
$462$	−0.506559	−	0.0322598i	−0.0235672	−	0.00150086i
$463$	2.94388	−	2.94388i	0.136813	−	0.136813i	−0.635383	−	0.772197i	$-0.719158\pi$
$463$	2.94388	−	2.94388i	0.136813	−	0.136813i	0.772197	+	0.635383i	$0.219158\pi$
$464$		−	11.4983i		−	0.533797i
$465$	−0.119972	−	0.136292i	−0.00556356	−	0.00632038i
$466$	10.2488	−	10.2488i	0.474767	−	0.474767i
$467$	25.0862			1.16085			0.580424	−	0.814314i	$-0.302887\pi$
$467$	25.0862			1.16085			0.580424	+	0.814314i	$0.302887\pi$
$468$	−3.68134	+	1.04756i	−0.170170	+	0.0484235i
$469$	−8.82998			−0.407731
$470$	−3.72015	+	3.72015i	−0.171598	+	0.171598i
$471$	−21.3358	−	24.2381i	−0.983102	−	1.11683i
$472$		−	37.6907i		−	1.73486i
$473$	0.624101	−	0.624101i	0.0286962	−	0.0286962i
$474$	−16.7188	−	1.06473i	−0.767922	−	0.0489045i
$475$	0.0993842	−	0.0993842i	0.00456006	−	0.00456006i
$476$	0.799286	+	0.799286i	0.0366352	+	0.0366352i
$477$	−11.1717	−	1.42872i	−0.511519	−	0.0654167i
$478$		−	15.1036i		−	0.690822i
$479$	3.31172	+	3.31172i	0.151316	+	0.151316i	0.778706	−	0.627389i	$-0.215877\pi$
$479$	3.31172	+	3.31172i	0.151316	+	0.151316i	−0.627389	+	0.778706i	$0.715877\pi$
$480$	3.20017	−	2.81698i	0.146067	−	0.128577i
$481$	−3.41799	+	8.53351i	−0.155847	+	0.389095i
$482$		−	25.6383i		−	1.16779i
$483$	−1.83014	−	0.116551i	−0.0832744	−	0.00530327i
$484$	−3.87945			−0.176339
$485$	22.9227			1.04087
$486$	22.7172	+	7.47764i	1.03047	+	0.339193i
$487$	23.7954	+	23.7954i	1.07827	+	1.07827i	0.996665	+	0.0816059i	$0.0260049\pi$
$487$	23.7954	+	23.7954i	1.07827	+	1.07827i	0.0816059	+	0.996665i	$0.473995\pi$
$488$	−21.5829	−	21.5829i	−0.977014	−	0.977014i
$489$	−10.9365	−	0.696486i	−0.494568	−	0.0314962i
$490$	−1.90783			−0.0861869
$491$	−8.65445			−0.390570			−0.195285	−	0.980747i	$-0.562563\pi$
$491$	−8.65445			−0.390570			−0.195285	+	0.980747i	$0.562563\pi$
$492$	−0.211202	+	3.31640i	−0.00952173	+	0.149515i
$493$		−	8.01550i		−	0.361000i
$494$	−0.206958	+	0.0885827i	−0.00931147	+	0.00398552i
$495$	−0.0903928	+	0.706817i	−0.00406285	+	0.0317690i
$496$	0.273166	+	0.273166i	0.0122655	+	0.0122655i
$497$			10.3774i			0.465489i
$498$	22.2039	−	19.5452i	0.994982	−	0.875841i
$499$	1.17469	+	1.17469i	0.0525864	+	0.0525864i	0.732911	−	0.680325i	$-0.238161\pi$
$499$	1.17469	+	1.17469i	0.0525864	+	0.0525864i	−0.680325	+	0.732911i	$0.738161\pi$
$500$	−2.63027	+	2.63027i	−0.117629	+	0.117629i
$501$	−0.353482	+	5.55054i	−0.0157924	+	0.247980i
$502$	7.81366	−	7.81366i	0.348741	−	0.348741i
$503$		−	17.4205i		−	0.776742i	−0.921503	−	0.388371i	$-0.873038\pi$
$503$		−	17.4205i		−	0.776742i	0.921503	−	0.388371i	$-0.126962\pi$
$504$	−0.961134	+	7.51549i	−0.0428123	+	0.334766i
$505$	−5.17169	+	5.17169i	−0.230137	+	0.230137i
$506$	0.310278			0.0137936
$507$	22.4985	+	0.903570i	0.999195	+	0.0401289i
$508$	−3.98463			−0.176789
$509$	16.6981	−	16.6981i	0.740130	−	0.740130i	−0.232473	−	0.972603i	$-0.574682\pi$
$509$	16.6981	−	16.6981i	0.740130	−	0.740130i	0.972603	+	0.232473i	$0.0746816\pi$
$510$	7.92347	−	6.97470i	0.350857	−	0.308845i
$511$			0.650679i			0.0287843i
$512$	9.95321	−	9.95321i	0.439874	−	0.439874i
$513$	0.207625	+	0.0401016i	0.00916686	+	0.00177053i
$514$	−5.46601	+	5.46601i	−0.241096	+	0.241096i
$515$	−14.8267	−	14.8267i	−0.653342	−	0.653342i
$516$	1.87120	+	2.12575i	0.0823751	+	0.0935808i
$517$			0.526739i			0.0231659i
$518$	−2.76592	−	2.76592i	−0.121528	−	0.121528i
$519$	−22.5739	−	25.6447i	−0.990884	−	1.12568i
$520$	−10.4100	+	4.45572i	−0.456508	+	0.195396i
$521$		−	9.61958i		−	0.421442i	−0.977546	−	0.210721i	$-0.932419\pi$
$521$		−	9.61958i		−	0.421442i	0.977546	−	0.210721i	$-0.0675811\pi$
$522$	−9.13634	+	7.06447i	−0.399887	+	0.309203i
$523$	−25.4136			−1.11126			−0.555630	−	0.831430i	$-0.687523\pi$
$523$	−25.4136			−1.11126			−0.555630	+	0.831430i	$0.687523\pi$
$524$	2.53404			0.110700
$525$	0.380186	−	5.96985i	0.0165927	−	0.260546i
$526$	31.7526	+	31.7526i	1.38448	+	1.38448i
$527$	0.190424	+	0.190424i	0.00829501	+	0.00829501i
$528$	0.0963549	−	1.51301i	0.00419331	−	0.0658453i
$529$	−21.8790			−0.951261
$530$	7.16245			0.311117
$531$	−35.4181	+	27.3862i	−1.53701	+	1.18846i
$532$		−	0.0144003i		−	0.000624331i
$533$	7.26892	−	18.1479i	0.314852	−	0.786073i
$534$	−21.8072	−	24.7737i	−0.943692	−	1.07206i
$535$	14.4271	+	14.4271i	0.623736	+	0.623736i
$536$		−	22.3007i		−	0.963243i
$537$	17.3232	+	19.6797i	0.747550	+	0.849240i
$538$	17.9701	+	17.9701i	0.774744	+	0.774744i
$539$	−0.135065	+	0.135065i	−0.00581767	+	0.00581767i
$540$	−2.24491	−	0.433592i	−0.0966055	−	0.0186588i
$541$	4.26209	−	4.26209i	0.183242	−	0.183242i	−0.609525	−	0.792767i	$-0.708640\pi$
$541$	4.26209	−	4.26209i	0.183242	−	0.183242i	0.792767	+	0.609525i	$0.208640\pi$
$542$			17.4521i			0.749632i
$543$	15.2563	−	13.4294i	0.654709	−	0.576312i
$544$	−4.47122	+	4.47122i	−0.191702	+	0.191702i
$545$	20.1649			0.863771
$546$	−4.12059	+	8.64991i	−0.176345	+	0.370182i
$547$	−32.6626			−1.39655			−0.698275	−	0.715829i	$-0.746049\pi$
$547$	−32.6626			−1.39655			−0.698275	+	0.715829i	$0.746049\pi$
$548$	3.09910	−	3.09910i	0.132387	−	0.132387i
$549$	−4.59931	+	35.9638i	−0.196294	+	1.53490i
$550$			1.01212i			0.0431567i
$551$	−0.0722053	+	0.0722053i	−0.00307605	+	0.00307605i
$552$	0.294358	−	4.62215i	0.0125287	−	0.196732i
$553$	−4.45779	+	4.45779i	−0.189565	+	0.189565i
$554$	−25.7953	−	25.7953i	−1.09594	−	1.09594i
$555$	−4.12187	+	3.62831i	−0.174964	+	0.154013i
$556$		−	0.874611i		−	0.0370918i
$557$	29.8168	+	29.8168i	1.26338	+	1.26338i	0.949446	+	0.313932i	$0.101646\pi$
$557$	29.8168	+	29.8168i	1.26338	+	1.26338i	0.313932	+	0.949446i	$0.398354\pi$
$558$	0.0492215	−	0.384883i	0.00208371	−	0.0162934i
$559$	−6.55572	−	15.3163i	−0.277278	−	0.647810i
$560$		−	5.69838i		−	0.240800i
$561$	0.0671690	−	1.05472i	0.00283588	−	0.0445303i
$562$	14.6013			0.615920
$563$	31.4092			1.32374			0.661869	−	0.749620i	$-0.269763\pi$
$563$	31.4092			1.32374			0.661869	+	0.749620i	$0.269763\pi$
$564$	−1.68670	−	0.107416i	−0.0710230	−	0.00452305i
$565$	−2.48027	−	2.48027i	−0.104346	−	0.104346i
$566$	−29.8830	−	29.8830i	−1.25608	−	1.25608i
$567$	7.76069	−	4.55760i	0.325918	−	0.191401i
$568$	−26.2088			−1.09970
$569$	16.8044			0.704478			0.352239	−	0.935910i	$-0.385421\pi$
$569$	16.8044			0.704478			0.352239	+	0.935910i	$0.385421\pi$
$570$	−0.134206	−	0.00854679i	−0.00562126	−	0.000357986i
$571$			22.6238i			0.946778i	0.880854	+	0.473389i	$0.156969\pi$
$571$			22.6238i			0.946778i	−0.880854	+	0.473389i	$0.843031\pi$
$572$	0.0906117	−	0.226225i	0.00378867	−	0.00945895i
$573$	29.5123	−	25.9785i	1.23290	−	1.08527i
$574$	5.88219	+	5.88219i	0.245518	+	0.245518i
$575$			3.65667i			0.152494i
$576$	−18.2357	−	2.33211i	−0.759819	−	0.0971711i
$577$	−4.13433	−	4.13433i	−0.172115	−	0.172115i	0.615793	−	0.787908i	$-0.288836\pi$
$577$	−4.13433	−	4.13433i	−0.172115	−	0.172115i	−0.787908	+	0.615793i	$0.788836\pi$
$578$	7.37212	−	7.37212i	0.306640	−	0.306640i
$579$	44.5667	+	2.83820i	1.85213	+	0.117952i
$580$	0.780708	−	0.780708i	0.0324172	−	0.0324172i
$581$		−	11.1317i		−	0.461820i
$582$	32.3664	+	36.7692i	1.34163	+	1.52413i
$583$	0.507068	−	0.507068i	0.0210006	−	0.0210006i
$584$	−1.64333			−0.0680016
$585$	11.7510	+	6.54476i	0.485843	+	0.270592i
$586$	25.1003			1.03688
$587$	−3.68739	+	3.68739i	−0.152195	+	0.152195i	−0.779098	−	0.626903i	$-0.784322\pi$
$587$	−3.68739	+	3.68739i	−0.152195	+	0.152195i	0.626903	+	0.779098i	$0.284322\pi$
$588$	−0.404957	−	0.460044i	−0.0167002	−	0.0189719i
$589$		−	0.00343076i		−	0.000141362i
$590$	20.1326	−	20.1326i	0.828847	−	0.828847i
$591$	8.52026	+	0.542606i	0.350477	+	0.0223198i
$592$	8.26137	−	8.26137i	0.339540	−	0.339540i
$593$	6.58899	+	6.58899i	0.270577	+	0.270577i	0.829333	−	0.558755i	$-0.188721\pi$
$593$	6.58899	+	6.58899i	0.270577	+	0.270577i	−0.558755	+	0.829333i	$0.688721\pi$
$594$	−1.26141	+	0.853017i	−0.0517561	+	0.0349997i
$595$		−	3.97234i		−	0.162850i
$596$	1.12096	+	1.12096i	0.0459165	+	0.0459165i
$597$	0.846773	−	0.745378i	0.0346561	−	0.0305063i
$598$	2.17770	−	5.43695i	0.0890528	−	0.222333i
$599$		−	26.8219i		−	1.09591i	−0.836507	−	0.547957i	$-0.815406\pi$
$599$		−	26.8219i		−	1.09591i	0.836507	−	0.547957i	$-0.184594\pi$
$600$	15.0773	+	0.960184i	0.615527	+	0.0391993i
$601$	28.1716			1.14914			0.574572	−	0.818454i	$-0.305169\pi$
$601$	28.1716			1.14914			0.574572	+	0.818454i	$0.305169\pi$
$602$	7.08926			0.288937
$603$	−20.9560	+	16.2038i	−0.853395	+	0.659868i
$604$	−4.74733	−	4.74733i	−0.193166	−	0.193166i
$605$	9.64017	+	9.64017i	0.391929	+	0.391929i
$606$	−15.5980	−	0.993346i	−0.633625	−	0.0403519i
$607$	−4.60376			−0.186861			−0.0934303	−	0.995626i	$-0.529783\pi$
$607$	−4.60376			−0.186861			−0.0934303	+	0.995626i	$0.529783\pi$
$608$	0.0805554			0.00326695
$609$	−0.276215	+	4.33726i	−0.0111928	+	0.175755i
$610$		−	23.0572i		−	0.933558i
$611$	9.22994	+	3.69694i	0.373403	+	0.149562i
$612$	3.36369	+	0.430173i	0.135969	+	0.0173887i
$613$	19.5039	+	19.5039i	0.787755	+	0.787755i	0.981126	−	0.193371i	$-0.0619421\pi$
$613$	19.5039	+	19.5039i	0.787755	+	0.787755i	−0.193371	+	0.981126i	$0.561942\pi$
$614$			1.61907i			0.0653405i
$615$	8.76584	−	7.71620i	0.353473	−	0.311147i
$616$	−0.341116	−	0.341116i	−0.0137440	−	0.0137440i
$617$	24.6358	−	24.6358i	0.991799	−	0.991799i	−0.00816772	−	0.999967i	$-0.502600\pi$
$617$	24.6358	−	24.6358i	0.991799	−	0.991799i	0.999967	+	0.00816772i	$0.00259990\pi$
$618$	2.84782	−	44.7178i	0.114556	−	1.79881i
$619$	−4.23506	+	4.23506i	−0.170221	+	0.170221i	−0.787077	−	0.616855i	$-0.788406\pi$
$619$	−4.23506	+	4.23506i	−0.170221	+	0.170221i	0.616855	+	0.787077i	$0.288406\pi$
$620$			0.0370946i			0.00148975i
$621$	−4.55733	+	3.08186i	−0.182879	+	0.123671i
$622$	−14.3231	+	14.3231i	−0.574306	+	0.574306i
$623$	−12.4200			−0.497597
$624$	−25.8359	−	12.3075i	−1.03426	−	0.492696i
$625$	−4.19630			−0.167852
$626$	−13.1621	+	13.1621i	−0.526065	+	0.526065i
$627$	−0.0101062	+	0.00889606i	−0.000403603	+	0.000355275i
$628$			6.59690i			0.263245i
$629$	5.75901	−	5.75901i	0.229627	−	0.229627i
$630$	−4.52781	+	3.50103i	−0.180392	+	0.139484i
$631$	−8.38462	+	8.38462i	−0.333786	+	0.333786i	−0.854022	−	0.520236i	$-0.825844\pi$
$631$	−8.38462	+	8.38462i	−0.333786	+	0.333786i	0.520236	+	0.854022i	$0.325844\pi$
$632$	−11.2585	−	11.2585i	−0.447837	−	0.447837i
$633$	16.8260	+	19.1149i	0.668775	+	0.759750i
$634$		−	48.7661i		−	1.93675i
$635$	9.90152	+	9.90152i	0.392930	+	0.392930i
$636$	1.52031	+	1.72712i	0.0602842	+	0.0684847i
$637$	1.41876	+	3.31468i	0.0562133	+	0.131332i
$638$		−	0.735329i		−	0.0291120i
$639$	19.0434	+	24.6285i	0.753345	+	0.974287i
$640$	16.6142			0.656735
$641$	9.53131			0.376464			0.188232	−	0.982125i	$-0.439724\pi$
$641$	9.53131			0.376464			0.188232	+	0.982125i	$0.439724\pi$
$642$	−2.77106	+	43.5125i	−0.109365	+	1.71730i
$643$	−27.1746	−	27.1746i	−1.07166	−	1.07166i	−0.997226	−	0.0744374i	$-0.976284\pi$
$643$	−27.1746	−	27.1746i	−1.07166	−	1.07166i	−0.0744374	−	0.997226i	$-0.523716\pi$
$644$	0.264916	+	0.264916i	0.0104392	+	0.0104392i
$645$	0.632521	−	9.93215i	0.0249055	−	0.391078i
$646$	0.199451			0.00784730
$647$	−42.0485			−1.65310			−0.826548	−	0.562866i	$-0.809699\pi$
$647$	−42.0485			−1.65310			−0.826548	+	0.562866i	$0.809699\pi$
$648$	11.5105	+	19.6001i	0.452176	+	0.769966i
$649$		−	2.85059i		−	0.111895i
$650$	17.7351	+	7.10358i	0.695628	+	0.278625i
$651$	−0.0964782	−	0.109602i	−0.00378128	−	0.00429565i
$652$	1.58308	+	1.58308i	0.0619983	+	0.0619983i
$653$			2.44638i			0.0957341i	0.998854	+	0.0478671i	$0.0152424\pi$
$653$			2.44638i			0.0957341i	−0.998854	+	0.0478671i	$0.984758\pi$
$654$	28.4725	+	32.3457i	1.11336	+	1.26482i
$655$	−6.29693	−	6.29693i	−0.246041	−	0.246041i
$656$	−17.5692	+	17.5692i	−0.685961	+	0.685961i
$657$	1.19405	+	1.54424i	0.0465844	+	0.0602467i
$658$	−2.99165	+	2.99165i	−0.116627	+	0.116627i
$659$			47.4472i			1.84828i	0.382052	+	0.924141i	$0.375217\pi$
$659$			47.4472i			1.84828i	−0.382052	+	0.924141i	$0.624783\pi$
$660$	0.109272	−	0.0961873i	0.00425340	−	0.00374408i
$661$	−14.9156	+	14.9156i	−0.580150	+	0.580150i	−0.934944	−	0.354795i	$-0.884551\pi$
$661$	−14.9156	+	14.9156i	−0.580150	+	0.580150i	0.354795	+	0.934944i	$0.384551\pi$
$662$	−22.0109			−0.855477
$663$	−18.0102	−	8.57959i	−0.699459	−	0.333204i
$664$	28.1138			1.09103
$665$	−0.0357837	+	0.0357837i	−0.00138763	+	0.00138763i
$666$	−11.6400	−	1.48861i	−0.451041	−	0.0576824i
$667$		−	2.65667i		−	0.102867i
$668$	0.803450	−	0.803450i	0.0310864	−	0.0310864i
$669$	−2.80822	+	44.0961i	−0.108572	+	1.70485i
$670$	11.9120	−	11.9120i	0.460200	−	0.460200i
$671$	−1.63234	−	1.63234i	−0.0630158	−	0.0630158i
$672$	2.57350	−	2.26534i	0.0992748	−	0.0873874i
$673$			12.4111i			0.478414i	0.970969	+	0.239207i	$0.0768874\pi$
$673$			12.4111i			0.478414i	−0.970969	+	0.239207i	$0.923113\pi$
$674$	18.4885	+	18.4885i	0.712149	+	0.712149i
$675$	−10.0529	−	14.8658i	−0.386936	−	0.572186i
$676$	−3.32814	−	3.17554i	−0.128005	−	0.122136i
$677$		−	24.8760i		−	0.956061i	−0.878343	−	0.478031i	$-0.841351\pi$
$677$		−	24.8760i		−	0.956061i	0.878343	−	0.478031i	$-0.158649\pi$
$678$	0.476395	−	7.48058i	0.0182958	−	0.287290i
$679$	18.4338			0.707426
$680$	10.0324			0.384725
$681$	30.3725	+	1.93425i	1.16388	+	0.0741206i
$682$	0.0174692	+	0.0174692i	0.000668931	+	0.000668931i
$683$	20.7208	+	20.7208i	0.792859	+	0.792859i	0.981958	−	0.189099i	$-0.0605567\pi$
$683$	20.7208	+	20.7208i	0.792859	+	0.792859i	−0.189099	+	0.981958i	$0.560557\pi$
$684$	−0.0264257	−	0.0341759i	−0.00101041	−	0.00130675i
$685$	−15.4021			−0.588484
$686$	−1.53423			−0.0585770
$687$	−8.32146	−	0.529946i	−0.317484	−	0.0202187i
$688$			21.1745i			0.807270i
$689$	−5.32637	−	12.4441i	−0.202919	−	0.474083i
$690$	2.62617	−	2.31170i	0.0999764	−	0.0880049i
$691$	22.6045	+	22.6045i	0.859916	+	0.859916i	0.991328	−	0.131412i	$-0.0419511\pi$
$691$	22.6045	+	22.6045i	0.859916	+	0.859916i	−0.131412	+	0.991328i	$0.541951\pi$
$692$			6.97972i			0.265329i
$693$	−0.0726915	+	0.568404i	−0.00276132	+	0.0215919i
$694$	24.8431	+	24.8431i	0.943031	+	0.943031i
$695$	−2.17335	+	2.17335i	−0.0824398	+	0.0824398i
$696$	−10.9540	−	0.697599i	−0.415212	−	0.0264424i
$697$	−12.2475	+	12.2475i	−0.463906	+	0.463906i
$698$		−	4.60020i		−	0.174120i
$699$	−10.8116	−	12.2823i	−0.408931	−	0.464558i
$700$	−0.864147	+	0.864147i	−0.0326617	+	0.0326617i
$701$	−32.9524			−1.24460			−0.622298	−	0.782780i	$-0.713801\pi$
$701$	−32.9524			−1.24460			−0.622298	+	0.782780i	$0.713801\pi$
$702$	6.09402	+	28.0903i	0.230004	+	1.06020i
$703$	−0.103757			−0.00391326
$704$	0.827688	−	0.827688i	0.0311947	−	0.0311947i
$705$	3.92442	+	4.45826i	0.147802	+	0.167908i
$706$		−	8.01495i		−	0.301647i
$707$	−4.15894	+	4.15894i	−0.156413	+	0.156413i
$708$	9.12805	+	0.581313i	0.343053	+	0.0218471i
$709$	12.9320	−	12.9320i	0.485671	−	0.485671i	−0.421266	−	0.906937i	$-0.638414\pi$
$709$	12.9320	−	12.9320i	0.485671	−	0.485671i	0.906937	+	0.421266i	$0.138414\pi$
$710$	−13.9995	−	13.9995i	−0.525391	−	0.525391i
$711$	−2.39917	+	18.7600i	−0.0899758	+	0.703556i
$712$		−	31.3676i		−	1.17555i
$713$	0.0631144	+	0.0631144i	0.00236365	+	0.00236365i
$714$	6.37185	−	5.60887i	0.238461	−	0.209907i
$715$	−0.787318	+	0.336990i	−0.0294440	+	0.0126027i
$716$		−	5.35622i		−	0.200171i
$717$	−17.0166	−	1.08369i	−0.635496	−	0.0404711i
$718$	−46.7320			−1.74402
$719$	−21.3429			−0.795954			−0.397977	−	0.917395i	$-0.630288\pi$
$719$	−21.3429			−0.795954			−0.397977	+	0.917395i	$0.630288\pi$
$720$	−10.4570	−	13.5239i	−0.389710	−	0.504004i
$721$	−11.9232	−	11.9232i	−0.444045	−	0.444045i
$722$	20.6106	+	20.6106i	0.767046	+	0.767046i
$723$	−28.8856	−	1.83955i	−1.07427	−	0.0684138i
$724$	−4.15230			−0.154319
$725$	8.66594			0.321845
$726$	−1.85162	+	29.0751i	−0.0687202	+	1.07908i
$727$		−	2.51935i		−	0.0934374i	−0.998908	−	0.0467187i	$-0.985124\pi$
$727$		−	2.51935i		−	0.0934374i	0.998908	−	0.0467187i	$-0.0148764\pi$
$728$	−8.37145	+	3.58317i	−0.310266	+	0.132801i
$729$	10.0547	−	25.0580i	0.372397	−	0.928074i
$730$	−0.877791	−	0.877791i	−0.0324885	−	0.0324885i
$731$			14.7608i			0.545946i
$732$	5.55990	−	4.89414i	0.205500	−	0.180893i
$733$	−14.7122	−	14.7122i	−0.543407	−	0.543407i	0.381119	−	0.924526i	$-0.375539\pi$
$733$	−14.7122	−	14.7122i	−0.543407	−	0.543407i	−0.924526	+	0.381119i	$0.875539\pi$
$734$	−17.4756	+	17.4756i	−0.645035	+	0.645035i
$735$	−0.136887	+	2.14947i	−0.00504917	+	0.0792844i
$736$	−1.48195	+	1.48195i	−0.0546253	+	0.0546253i
$737$		−	1.68662i		−	0.0621276i
$738$	24.7544	+	3.16577i	0.911222	+	0.116534i
$739$	5.25700	−	5.25700i	0.193382	−	0.193382i	−0.603774	−	0.797156i	$-0.706337\pi$
$739$	5.25700	−	5.25700i	0.193382	−	0.193382i	0.797156	+	0.603774i	$0.206337\pi$
$740$	1.12185			0.0412401
$741$	0.0849531	+	0.239527i	0.00312083	+	0.00879923i
$742$	5.75986			0.211451
$743$	3.11030	−	3.11030i	0.114106	−	0.114106i	−0.647749	−	0.761854i	$-0.724289\pi$
$743$	3.11030	−	3.11030i	0.114106	−	0.114106i	0.761854	+	0.647749i	$0.224289\pi$
$744$	0.276808	−	0.243662i	0.0101483	−	0.00893309i
$745$		−	5.57103i		−	0.204107i
$746$	13.1023	−	13.1023i	0.479711	−	0.479711i
$747$	−20.4276	−	26.4186i	−0.747407	−	0.966607i
$748$	−0.152672	+	0.152672i	−0.00558226	+	0.00558226i
$749$	11.6019	+	11.6019i	0.423923	+	0.423923i
$750$	18.4576	+	20.9684i	0.673974	+	0.765656i
$751$		−	26.8567i		−	0.980013i	−0.871719	−	0.490007i	$-0.836994\pi$
$751$		−	26.8567i		−	0.980013i	0.871719	−	0.490007i	$-0.163006\pi$
$752$	−8.93559	−	8.93559i	−0.325847	−	0.325847i
$753$	−8.24269	−	9.36396i	−0.300380	−	0.341242i
$754$	−12.8850	−	5.16094i	−0.469245	−	0.187950i
$755$			23.5936i			0.858659i
$756$	−1.80530	−	0.348683i	−0.0656581	−	0.0126815i
$757$	−11.2616			−0.409310			−0.204655	−	0.978834i	$-0.565607\pi$
$757$	−11.2616			−0.409310			−0.204655	+	0.978834i	$0.565607\pi$
$758$	7.02895			0.255303
$759$	0.0222626	−	0.349578i	0.000808080	−	0.0126889i
$760$	−0.0903740	−	0.0903740i	−0.00327821	−	0.00327821i
$761$	−36.7325	−	36.7325i	−1.33155	−	1.33155i	−0.903981	−	0.427572i	$-0.859369\pi$
$761$	−36.7325	−	36.7325i	−1.33155	−	1.33155i	−0.427572	−	0.903981i	$-0.640631\pi$
$762$	−1.90182	+	29.8633i	−0.0688958	+	1.08183i
$763$	16.2161			0.587063
$764$	−8.03239			−0.290602
$765$	−7.28959	−	9.42748i	−0.263556	−	0.340851i
$766$		−	32.6664i		−	1.18028i
$767$	−49.9503	−	20.0070i	−1.80360	−	0.722410i
$768$	9.43269	+	10.7158i	0.340373	+	0.386674i
$769$	−25.2159	−	25.2159i	−0.909308	−	0.909308i	0.0869081	−	0.996216i	$-0.472301\pi$
$769$	−25.2159	−	25.2159i	−0.909308	−	0.909308i	−0.996216	+	0.0869081i	$0.972301\pi$
$770$		−	0.364416i		−	0.0131326i
$771$	5.76614	+	6.55052i	0.207663	+	0.235911i
$772$	−6.45111	−	6.45111i	−0.232181	−	0.232181i
$773$	22.5319	−	22.5319i	0.810417	−	0.810417i	−0.174279	−	0.984696i	$-0.555759\pi$
$773$	22.5319	−	22.5319i	0.810417	−	0.810417i	0.984696	+	0.174279i	$0.0557594\pi$
$774$	16.8248	−	13.0094i	0.604755	−	0.467613i
$775$	−0.205877	+	0.205877i	−0.00739531	+	0.00739531i
$776$			46.5559i			1.67126i
$777$	−3.31471	+	2.91779i	−0.118914	+	0.104675i
$778$	41.7363	−	41.7363i	1.49632	−	1.49632i
$779$	0.220656			0.00790581
$780$	−0.918542	−	2.58984i	−0.0328891	−	0.0927312i
$781$	−1.98220			−0.0709285
$782$	−3.66923	+	3.66923i	−0.131211	+	0.131211i
$783$	7.30371	+	10.8004i	0.261013	+	0.385975i
$784$		−	4.58249i		−	0.163660i
$785$	16.3929	−	16.3929i	0.585086	−	0.585086i
$786$	1.20948	−	18.9918i	0.0431405	−	0.677413i
$787$	−26.1974	+	26.1974i	−0.933835	+	0.933835i	−0.997943	−	0.0641082i	$-0.979580\pi$
$787$	−26.1974	+	26.1974i	−0.933835	+	0.933835i	0.0641082	+	0.997943i	$0.479580\pi$
$788$	−1.23332	−	1.23332i	−0.0439353	−	0.0439353i
$789$	38.0526	−	33.4961i	1.35471	−	1.19249i
$790$		−	12.0275i		−	0.427918i
$791$	−1.99457	−	1.99457i	−0.0709187	−	0.0709187i
$792$	−1.43554	−	0.183587i	−0.0510097	−	0.00652349i
$793$	−40.0598	+	17.1465i	−1.42257	+	0.608891i
$794$		−	0.757844i		−	0.0268949i
$795$	0.513909	−	8.06964i	0.0182265	−	0.286201i
$796$	−0.230467			−0.00816867
$797$	31.2383			1.10652			0.553259	−	0.833009i	$-0.313384\pi$
$797$	31.2383			1.10652			0.553259	+	0.833009i	$0.313384\pi$
$798$	−0.107925	−	0.00687311i	−0.00382050	−	0.000243306i
$799$	−6.22900	−	6.22900i	−0.220366	−	0.220366i
$800$	−4.83405	−	4.83405i	−0.170910	−	0.170910i
$801$	−29.4762	+	22.7918i	−1.04149	+	0.805308i
$802$	−27.7821			−0.981021
$803$	−0.124287			−0.00438599
$804$	5.40085	+	0.343949i	0.190473	+	0.0121301i
$805$		−	1.31660i		−	0.0464040i
$806$	0.428718	−	0.183501i	0.0151009	−	0.00646355i
$807$	21.5355	−	18.9568i	0.758085	−	0.667309i
$808$	−10.5037	−	10.5037i	−0.369518	−	0.369518i
$809$			27.2948i			0.959634i	0.877369	+	0.479817i	$0.159297\pi$
$809$			27.2948i			0.959634i	−0.877369	+	0.479817i	$0.840703\pi$
$810$	−4.32109	+	16.6178i	−0.151828	+	0.583891i
$811$	12.9506	+	12.9506i	0.454758	+	0.454758i	0.896930	−	0.442172i	$-0.145792\pi$
$811$	12.9506	+	12.9506i	0.454758	+	0.454758i	−0.442172	+	0.896930i	$0.645792\pi$
$812$	0.627826	−	0.627826i	0.0220324	−	0.0220324i
$813$	19.6626	+	1.25219i	0.689596	+	0.0439164i
$814$	0.528322	−	0.528322i	0.0185177	−	0.0185177i
$815$		−	7.86771i		−	0.275594i
$816$	16.7528	+	19.0317i	0.586466	+	0.666243i
$817$	0.132968	−	0.132968i	0.00465196	−	0.00465196i
$818$	−34.8675			−1.21911
$819$	9.44984	+	5.26313i	0.330204	+	0.183909i
$820$	−2.38580			−0.0833159
$821$	0.576885	−	0.576885i	0.0201334	−	0.0201334i	−0.696968	−	0.717102i	$-0.745468\pi$
$821$	0.576885	−	0.576885i	0.0201334	−	0.0201334i	0.717102	+	0.696968i	$0.245468\pi$
$822$	−21.7475	−	24.7058i	−0.758530	−	0.861714i
$823$			21.1292i			0.736517i	0.929723	+	0.368259i	$0.120046\pi$
$823$			21.1292i			0.736517i	−0.929723	+	0.368259i	$0.879954\pi$
$824$	30.1129	−	30.1129i	1.04903	−	1.04903i
$825$	1.14031	+	0.0726197i	0.0397004	+	0.00252829i
$826$	16.1901	−	16.1901i	0.563327	−	0.563327i
$827$	−11.1442	−	11.1442i	−0.387520	−	0.387520i	0.486282	−	0.873802i	$-0.338353\pi$
$827$	−11.1442	−	11.1442i	−0.387520	−	0.387520i	−0.873802	+	0.486282i	$0.838353\pi$
$828$	1.11486	+	0.142577i	0.0387442	+	0.00495489i
$829$			28.8835i			1.00317i	0.865110	+	0.501583i	$0.167249\pi$
$829$			28.8835i			1.00317i	−0.865110	+	0.501583i	$0.832751\pi$
$830$	15.0171	+	15.0171i	0.521250	+	0.521250i
$831$	−30.9133	+	27.2117i	−1.07237	+	0.943963i
$832$	−8.69425	−	20.3126i	−0.301419	−	0.704212i
$833$		−	3.19446i		−	0.110681i
$834$	−6.55490	−	0.417444i	−0.226978	−	0.0144549i
$835$	−3.99304			−0.138185
$836$	0.00275061			9.51319e−5
$837$	−0.430100	−	0.0830713i	−0.0148664	−	0.00287137i
$838$	−15.0247	−	15.0247i	−0.519019	−	0.519019i
$839$	17.7174	+	17.7174i	0.611673	+	0.611673i	0.943382	−	0.331709i	$-0.107625\pi$
$839$	17.7174	+	17.7174i	0.611673	+	0.611673i	−0.331709	+	0.943382i	$0.607625\pi$
$840$	−5.42863	−	0.345718i	−0.187305	−	0.0119284i
$841$	22.7040			0.782895
$842$	−0.429408			−0.0147984
$843$	1.04765	−	16.4507i	0.0360830	−	0.566593i
$844$		−	5.20251i		−	0.179078i
$845$	0.379189	+	16.1612i	0.0130445	+	0.555962i
$846$	−1.61009	+	12.5900i	−0.0553562	+	0.432852i
$847$	7.75238	+	7.75238i	0.266375	+	0.266375i
$848$			17.2038i			0.590781i
$849$	−35.8121	+	31.5238i	−1.22907	+	1.08190i
$850$	−11.9689	−	11.9689i	−0.410529	−	0.410529i
$851$	1.90877	−	1.90877i	0.0654319	−	0.0654319i
$852$	0.404224	−	6.34732i	0.0138485	−	0.217455i
$853$	−14.7213	+	14.7213i	−0.504049	+	0.504049i	−0.912694	−	0.408645i	$-0.866002\pi$
$853$	−14.7213	+	14.7213i	−0.504049	+	0.504049i	0.408645	+	0.912694i	$0.366002\pi$
$854$		−	18.5420i		−	0.634494i
$855$	−0.0192586	+	0.150591i	−0.000658631	+	0.00515010i
$856$	−29.3013	+	29.3013i	−1.00150	+	1.00150i
$857$	−51.6376			−1.76391			−0.881954	−	0.471336i	$-0.843772\pi$
$857$	−51.6376			−1.76391			−0.881954	+	0.471336i	$0.843772\pi$
$858$	−1.65223	−	0.787077i	−0.0564062	−	0.0268704i
$859$	−41.6053			−1.41956			−0.709778	−	0.704426i	$-0.751205\pi$
$859$	−41.6053			−1.41956			−0.709778	+	0.704426i	$0.751205\pi$
$860$	−1.43769	+	1.43769i	−0.0490250	+	0.0490250i
$861$	7.04927	−	6.20517i	0.240238	−	0.211472i
$862$		−	7.32068i		−	0.249343i
$863$	−11.1546	+	11.1546i	−0.379707	+	0.379707i	−0.870996	−	0.491289i	$-0.836526\pi$
$863$	−11.1546	+	11.1546i	−0.379707	+	0.379707i	0.491289	+	0.870996i	$0.336526\pi$
$864$	1.95054	−	10.0989i	0.0663588	−	0.343571i
$865$	17.3441	−	17.3441i	0.589718	−	0.589718i
$866$	3.68892	+	3.68892i	0.125355	+	0.125355i
$867$	−7.77691	−	8.83482i	−0.264118	−	0.300046i
$868$			0.0298305i			0.00101251i
$869$	−0.851488	−	0.851488i	−0.0288847	−	0.0288847i
$870$	−5.47850	−	6.22375i	−0.185739	−	0.211005i
$871$	−29.5544	−	11.8376i	−1.00141	−	0.401103i
$872$			40.9549i			1.38691i
$873$	43.7487	−	33.8277i	1.48067	−	1.14489i
$874$	0.0661064			0.00223608
$875$	10.5122			0.355379
$876$	0.0253455	−	0.397987i	0.000856345	−	0.0134467i
$877$	−27.9561	−	27.9561i	−0.944010	−	0.944010i	0.0545033	−	0.998514i	$-0.482642\pi$
$877$	−27.9561	−	27.9561i	−0.944010	−	0.944010i	−0.998514	+	0.0545033i	$0.982642\pi$
$878$	8.20704	+	8.20704i	0.276974	+	0.276974i
$879$	1.80095	−	28.2794i	0.0607446	−	0.953841i
$880$	1.08845			0.0366918
$881$	−26.0001			−0.875965			−0.437983	−	0.898983i	$-0.644307\pi$
$881$	−26.0001			−0.875965			−0.437983	+	0.898983i	$0.644307\pi$
$882$	−3.64115	+	2.81544i	−0.122604	+	0.0948007i
$883$		−	48.0696i		−	1.61767i	−0.588036	−	0.808835i	$-0.700099\pi$
$883$		−	48.0696i		−	1.61767i	0.588036	−	0.808835i	$-0.299901\pi$
$884$	1.60371	+	3.74679i	0.0539387	+	0.126018i
$885$	−21.2381	−	24.1271i	−0.713909	−	0.811024i
$886$	−28.9079	−	28.9079i	−0.971179	−	0.971179i
$887$		−	35.9526i		−	1.20717i	−0.797298	−	0.603586i	$-0.793738\pi$
$887$		−	35.9526i		−	1.20717i	0.797298	−	0.603586i	$-0.206262\pi$
$888$	−7.36908	−	8.37151i	−0.247290	−	0.280929i
$889$	7.96255	+	7.96255i	0.267055	+	0.267055i
$890$	16.7551	−	16.7551i	0.561631	−	0.561631i
$891$	0.870552	+	1.48238i	0.0291646	+	0.0496615i
$892$	6.38298	−	6.38298i	0.213718	−	0.213718i
$893$			0.112224i			0.00375544i
$894$	8.93625	−	7.86619i	0.298873	−	0.263085i
$895$	−13.3098	+	13.3098i	−0.444899	+	0.444899i
$896$	13.3607			0.446351
$897$	−5.96933	−	2.84363i	−0.199310	−	0.0949460i
$898$	16.9316			0.565014
$899$	0.149575	−	0.149575i	0.00498861	−	0.00498861i
$900$	−0.465080	+	3.63665i	−0.0155027	+	0.121222i
$901$			11.9928i			0.399537i
$902$	−1.12356	+	1.12356i	−0.0374106	+	0.0374106i
$903$	0.508657	−	7.98718i	0.0169271	−	0.265797i
$904$	5.03742	−	5.03742i	0.167542	−	0.167542i
$905$	10.3182	+	10.3182i	0.342988	+	0.342988i
$906$	−37.8454	+	33.3137i	−1.25733	+	1.10677i
$907$		−	15.7652i		−	0.523475i	−0.965139	−	0.261738i	$-0.915705\pi$
$907$		−	15.7652i		−	0.523475i	0.965139	−	0.261738i	$-0.0842955\pi$
$908$	−4.39647	−	4.39647i	−0.145902	−	0.145902i
$909$	−2.23832	+	17.5023i	−0.0742405	+	0.580516i
$910$	−6.38559	−	2.55767i	−0.211680	−	0.0847860i
$911$			31.5266i			1.04452i	0.852785	+	0.522261i	$0.174911\pi$
$911$			31.5266i			1.04452i	−0.852785	+	0.522261i	$0.825089\pi$
$912$	0.0205289	−	0.322355i	0.000679780	−	0.0106742i
$913$	2.12628			0.0703695
$914$	−23.3722			−0.773085
$915$	−25.9776	−	1.65436i	−0.858792	−	0.0546915i
$916$	1.20455	+	1.20455i	0.0397993	+	0.0397993i
$917$	−5.06383	−	5.06383i	−0.167222	−	0.167222i
$918$	4.82945	−	25.0043i	0.159395	−	0.825266i
$919$	45.2241			1.49181			0.745903	−	0.666055i	$-0.232018\pi$
$919$	45.2241			1.49181			0.745903	+	0.666055i	$0.232018\pi$
$920$	3.32515			0.109627
$921$	1.82414	+	0.116169i	0.0601076	+	0.00382790i
$922$			12.1032i			0.398597i
$923$	−13.9121	+	34.7336i	−0.457923	+	1.14327i
$924$	0.0878736	−	0.0773514i	0.00289083	−	0.00254467i
$925$	6.22634	+	6.22634i	0.204721	+	0.204721i
$926$			6.38740i			0.209903i
$927$	−50.1774	−	6.41704i	−1.64804	−	0.210763i
$928$	3.51207	+	3.51207i	0.115289	+	0.115289i
$929$	16.6527	−	16.6527i	0.546356	−	0.546356i	−0.379029	−	0.925385i	$-0.623742\pi$
$929$	16.6527	−	16.6527i	0.546356	−	0.546356i	0.925385	+	0.379029i	$0.123742\pi$
$930$	0.278011	+	0.0177049i	0.00911633	+	0.000580566i
$931$	−0.0287763	+	0.0287763i	−0.000943106	+	0.000943106i
$932$			3.34287i			0.109499i
$933$	15.1096	+	17.1650i	0.494666	+	0.561956i
$934$	−27.2150	+	27.2150i	−0.890502	+	0.890502i
$935$	0.758761			0.0248141
$936$	−13.2924	+	23.8662i	−0.434475	+	0.780091i
$937$	32.9591			1.07673			0.538363	−	0.842713i	$-0.319043\pi$
$937$	32.9591			1.07673			0.538363	+	0.842713i	$0.319043\pi$
$938$	9.57931	−	9.57931i	0.312776	−	0.312776i
$939$	13.8848	+	15.7736i	0.453115	+	0.514752i
$940$		−	1.21341i		−	0.0395770i
$941$	10.2529	−	10.2529i	0.334236	−	0.334236i	−0.519957	−	0.854193i	$-0.674052\pi$
$941$	10.2529	−	10.2529i	0.334236	−	0.334236i	0.854193	+	0.519957i	$0.174052\pi$
$942$	49.4414	+	3.14864i	1.61089	+	0.102588i
$943$	−4.05932	+	4.05932i	−0.132190	+	0.132190i
$944$	48.3574	+	48.3574i	1.57390	+	1.57390i
$945$	3.61959	+	5.35250i	0.117745	+	0.174117i
$946$			1.35413i			0.0440265i
$947$	−29.7312	−	29.7312i	−0.966133	−	0.966133i	0.0333124	−	0.999445i	$-0.489394\pi$
$947$	−29.7312	−	29.7312i	−0.966133	−	0.966133i	−0.999445	+	0.0333124i	$0.989394\pi$
$948$	2.90025	−	2.55296i	0.0941956	−	0.0829164i
$949$	−0.872313	+	2.17785i	−0.0283165	+	0.0706962i
$950$			0.215636i			0.00699617i
$951$	−54.9428	−	3.49899i	−1.78164	−	0.113462i
$952$	8.06781			0.261479
$953$	39.8792			1.29181			0.645907	−	0.763416i	$-0.276479\pi$
$953$	39.8792			1.29181			0.645907	+	0.763416i	$0.276479\pi$
$954$	13.6698	−	10.5698i	0.442575	−	0.342211i
$955$	19.9599	+	19.9599i	0.645888	+	0.645888i
$956$	2.46318	+	2.46318i	0.0796649	+	0.0796649i
$957$	−0.828465	−	0.0527601i	−0.0267805	−	0.00170549i
$958$	−7.18552			−0.232154
$959$	−12.3860			−0.399964
$960$	0.838854	−	13.1721i	0.0270739	−	0.425127i
$961$		−	30.9929i		−	0.999771i
$962$	−5.54963	−	12.9657i	−0.178927	−	0.418032i
$963$	48.8249	+	6.24408i	1.57336	+	0.201213i
$964$	4.18123	+	4.18123i	0.134668	+	0.134668i
$965$			32.0611i			1.03208i
$966$	2.11189	−	1.85901i	0.0679491	−	0.0598127i
$967$	32.1762	+	32.1762i	1.03472	+	1.03472i	0.999375	+	0.0353415i	$0.0112519\pi$
$967$	32.1762	+	32.1762i	1.03472	+	1.03472i	0.0353415	+	0.999375i	$0.488748\pi$
$968$	−19.5791	+	19.5791i	−0.629297	+	0.629297i
$969$	0.0143107	−	0.224713i	0.000459726	−	0.00721884i
$970$	−24.8679	+	24.8679i	−0.798462	+	0.798462i
$971$			47.3579i			1.51979i	0.650047	+	0.759894i	$0.274749\pi$
$971$			47.3579i			1.51979i	−0.650047	+	0.759894i	$0.725251\pi$
$972$	−4.92434	+	2.48535i	−0.157948	+	0.0797177i
$973$	−1.74775	+	1.74775i	−0.0560303	+	0.0560303i
$974$	−51.6294			−1.65431
$975$	9.27580	−	19.4717i	0.297063	−	0.623594i
$976$	55.3820			1.77273
$977$	5.65121	−	5.65121i	0.180798	−	0.180798i	−0.610905	−	0.791704i	$-0.709194\pi$
$977$	5.65121	−	5.65121i	0.180798	−	0.180798i	0.791704	+	0.610905i	$0.209194\pi$
$978$	12.6202	−	11.1091i	0.403551	−	0.355228i
$979$		−	2.37236i		−	0.0758210i
$980$	0.311139	−	0.311139i	0.00993899	−	0.00993899i
$981$	38.4854	−	29.7580i	1.22874	−	0.950099i
$982$	9.38889	−	9.38889i	0.299611	−	0.299611i
$983$	−5.63320	−	5.63320i	−0.179671	−	0.179671i	0.611541	−	0.791213i	$-0.290550\pi$
$983$	−5.63320	−	5.63320i	−0.179671	−	0.179671i	−0.791213	+	0.611541i	$0.790550\pi$
$984$	15.6716	+	17.8034i	0.499591	+	0.567551i
$985$			6.12944i			0.195300i
$986$	8.69571	+	8.69571i	0.276928	+	0.276928i
$987$	3.15592	+	3.58522i	0.100454	+	0.114119i
$988$	0.0193053	−	0.0481984i	0.000614183	−	0.00153340i
$989$			4.89232i			0.155567i
$990$	−0.668735	−	0.864862i	−0.0212538	−	0.0274871i
$991$	−21.7165			−0.689847			−0.344923	−	0.938631i	$-0.612095\pi$
$991$	−21.7165			−0.689847			−0.344923	+	0.938631i	$0.612095\pi$
$992$	−0.166872			−0.00529821
$993$	−1.57929	+	24.7987i	−0.0501172	+	0.786964i
$994$	−11.2580	−	11.2580i	−0.357083	−	0.357083i
$995$	0.572694	+	0.572694i	0.0181556	+	0.0181556i
$996$	−0.433606	+	6.80869i	−0.0137393	+	0.215741i
$997$	36.4221			1.15350			0.576750	−	0.816920i	$-0.304321\pi$
$997$	36.4221			1.15350			0.576750	+	0.816920i	$0.304321\pi$
$998$	−2.54875			−0.0806794
$999$	−2.51233	+	13.0075i	−0.0794866	+	0.411540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.n.c.8.7	✓	48
3.2	odd	2	inner	273.2.n.c.8.18	yes	48
13.5	odd	4	inner	273.2.n.c.239.18	yes	48
39.5	even	4	inner	273.2.n.c.239.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.n.c.8.7	✓	48	1.1	even	1	trivial
273.2.n.c.8.18	yes	48	3.2	odd	2	inner
273.2.n.c.239.7	yes	48	39.5	even	4	inner
273.2.n.c.239.18	yes	48	13.5	odd	4	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08486 + 1.08486i) q^{2} +(1.14443 + 1.30011i) q^{3} -0.353851i q^{4} +(-0.879295 + 0.879295i) q^{5} +(-2.65199 - 0.168890i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.78584 - 1.78584i) q^{8} +(-0.380562 + 2.97576i) q^{9} +O(q^{10})\)	\(q+(-1.08486 + 1.08486i) q^{2} +(1.14443 + 1.30011i) q^{3} -0.353851i q^{4} +(-0.879295 + 0.879295i) q^{5} +(-2.65199 - 0.168890i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.78584 - 1.78584i) q^{8} +(-0.380562 + 2.97576i) q^{9} -1.90783i q^{10} +(-0.135065 - 0.135065i) q^{11} +(0.460044 - 0.404957i) q^{12} +(-3.31468 + 1.41876i) q^{13} -1.53423i q^{14} +(-2.14947 - 0.136887i) q^{15} +4.58249 q^{16} +3.19446 q^{17} +(-2.81544 - 3.64115i) q^{18} +(-0.0287763 - 0.0287763i) q^{19} +(0.311139 + 0.311139i) q^{20} +(-1.72855 - 0.110081i) q^{21} +0.293054 q^{22} +1.05877 q^{23} +(0.278018 - 4.36556i) q^{24} +3.45368i q^{25} +(2.05681 - 5.13513i) q^{26} +(-4.30434 + 2.91078i) q^{27} +(0.250210 + 0.250210i) q^{28} -2.50919i q^{29} +(2.48038 - 2.18337i) q^{30} +(0.0596109 + 0.0596109i) q^{31} +(-1.39968 + 1.39968i) q^{32} +(0.0210267 - 0.330172i) q^{33} +(-3.46554 + 3.46554i) q^{34} -1.24351i q^{35} +(1.05298 + 0.134662i) q^{36} +(1.80281 - 1.80281i) q^{37} +0.0624367 q^{38} +(-5.63796 - 2.68577i) q^{39} +3.14057 q^{40} +(-3.83398 + 3.83398i) q^{41} +(1.99466 - 1.75581i) q^{42} +4.62074i q^{43} +(-0.0477930 + 0.0477930i) q^{44} +(-2.28195 - 2.95120i) q^{45} +(-1.14862 + 1.14862i) q^{46} +(-1.94994 - 1.94994i) q^{47} +(5.24434 + 5.95773i) q^{48} -1.00000i q^{49} +(-3.74677 - 3.74677i) q^{50} +(3.65583 + 4.15314i) q^{51} +(0.502030 + 1.17290i) q^{52} +3.75424i q^{53} +(1.51182 - 7.82741i) q^{54} +0.237524 q^{55} +2.52557 q^{56} +(0.00447986 - 0.0703448i) q^{57} +(2.72213 + 2.72213i) q^{58} +(10.5526 + 10.5526i) q^{59} +(-0.0484377 + 0.760592i) q^{60} +12.0856 q^{61} -0.129339 q^{62} +(-1.83509 - 2.37328i) q^{63} +6.12806i q^{64} +(1.66708 - 4.16209i) q^{65} +(0.335380 + 0.381002i) q^{66} +(6.24374 + 6.24374i) q^{67} -1.13036i q^{68} +(1.21169 + 1.37652i) q^{69} +(1.34904 + 1.34904i) q^{70} +(7.33792 - 7.33792i) q^{71} +(5.99388 - 4.63463i) q^{72} +(0.460100 - 0.460100i) q^{73} +3.91161i q^{74} +(-4.49016 + 3.95249i) q^{75} +(-0.0101825 + 0.0101825i) q^{76} +0.191011 q^{77} +(9.03010 - 3.20272i) q^{78} +6.30427 q^{79} +(-4.02936 + 4.02936i) q^{80} +(-8.71035 - 2.26493i) q^{81} -8.31867i q^{82} +(-7.87129 + 7.87129i) q^{83} +(-0.0389524 + 0.611649i) q^{84} +(-2.80887 + 2.80887i) q^{85} +(-5.01287 - 5.01287i) q^{86} +(3.26222 - 2.87159i) q^{87} +0.482411i q^{88} +(8.78228 + 8.78228i) q^{89} +(5.67725 + 0.726047i) q^{90} +(1.34062 - 3.34705i) q^{91} -0.374648i q^{92} +(-0.00928013 + 0.145721i) q^{93} +4.23083 q^{94} +0.0506058 q^{95} +(-3.42157 - 0.217900i) q^{96} +(-13.0347 - 13.0347i) q^{97} +(1.08486 + 1.08486i) q^{98} +(0.453323 - 0.350522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) \) 48 * q + 8 * q^3 + 4 * q^6	\( 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) \) 48 * q + 8 * q^3 + 4 * q^6 + 8 * q^13 - 16 * q^15 - 72 * q^16 - 12 * q^18 + 40 * q^19 + 16 * q^22 + 8 * q^24 - 16 * q^27 + 44 * q^33 - 32 * q^34 - 8 * q^37 - 4 * q^39 - 48 * q^40 - 8 * q^42 + 44 * q^45 - 32 * q^46 + 80 * q^48 - 72 * q^52 + 44 * q^54 - 80 * q^55 - 52 * q^57 + 16 * q^58 + 44 * q^60 - 64 * q^61 + 24 * q^63 - 152 * q^66 + 56 * q^67 + 16 * q^70 + 16 * q^72 + 32 * q^73 + 104 * q^76 - 44 * q^78 + 8 * q^79 + 12 * q^84 - 96 * q^85 - 72 * q^87 - 8 * q^91 - 8 * q^93 + 160 * q^94 + 8 * q^96 - 32 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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