LMFDB - Embedded newform 273.2.n.c.8.18

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			8.18
Character	$\chi$	$=$	273.8
Dual form			273.2.n.c.239.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08486 - 1.08486i) q^{2} +(1.14443 - 1.30011i) q^{3} -0.353851i q^{4} +(0.879295 - 0.879295i) q^{5} +(-0.168890 - 2.65199i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.78584 + 1.78584i) q^{8} +(-0.380562 - 2.97576i) q^{9} +O(q^{10})$	\(q+(1.08486 - 1.08486i) q^{2} +(1.14443 - 1.30011i) q^{3} -0.353851i q^{4} +(0.879295 - 0.879295i) q^{5} +(-0.168890 - 2.65199i) 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} +(-0.136887 - 2.14947i) q^{15} +4.58249 q^{16} -3.19446 q^{17} +(-3.64115 - 2.81544i) q^{18} +(-0.0287763 - 0.0287763i) q^{19} +(-0.311139 - 0.311139i) q^{20} +(0.110081 + 1.72855i) q^{21} +0.293054 q^{22} -1.05877 q^{23} +(4.36556 - 0.278018i) 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} +(0.330172 - 0.0210267i) 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} +(-1.94888 + 5.93312i) 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} +(-2.95120 - 2.28195i) 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} +(-7.82741 + 1.51182i) q^{54} +0.237524 q^{55} -2.52557 q^{56} +(-0.0703448 + 0.00447986i) q^{57} +(2.72213 + 2.72213i) q^{58} +(-10.5526 - 10.5526i) q^{59} +(-0.760592 + 0.0484377i) q^{60} +12.0856 q^{61} +0.129339 q^{62} +(2.37328 + 1.83509i) 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} +(4.63463 - 5.99388i) 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} +(4.32235 + 8.55088i) 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} +(0.611649 - 0.0389524i) 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} +(0.145721 - 0.00928013i) q^{93} +4.23083 q^{94} -0.0506058 q^{95} +(-0.217900 - 3.42157i) q^{96} +(-13.0347 - 13.0347i) q^{97} +(-1.08486 - 1.08486i) q^{98} +(0.350522 - 0.453323i) 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	−0.210484	−	0.977597i	$-0.567504\pi$
$2$	1.08486	−	1.08486i	0.767113	−	0.767113i	0.977597	+	0.210484i	$0.0675040\pi$
$3$	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	−0.482605	−	0.875838i	$-0.660309\pi$
$5$	0.879295	−	0.879295i	0.393233	−	0.393233i	0.875838	+	0.482605i	$0.160309\pi$
$6$	−0.168890	−	2.65199i	−0.0689489	−	1.08267i
$7$	−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	0.727175	−	0.686452i	$-0.240833\pi$
$11$	0.135065	+	0.135065i	0.0407237	+	0.0407237i	−0.686452	+	0.727175i	$0.740833\pi$
$12$	−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
$15$	−0.136887	−	2.14947i	−0.0353442	−	0.554991i
$16$	4.58249			1.14562
$17$	−3.19446			−0.774769			−0.387385	−	0.921918i	$-0.626621\pi$
$17$	−3.19446			−0.774769			−0.387385	+	0.921918i	$0.626621\pi$
$18$	−3.64115	−	2.81544i	−0.858227	−	0.663605i
$19$	−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
$21$	0.110081	+	1.72855i	0.0240217	+	0.377200i
$22$	0.293054			0.0624794
$23$	−1.05877			−0.220770			−0.110385	−	0.993889i	$-0.535208\pi$
$23$	−1.05877			−0.220770			−0.110385	+	0.993889i	$0.535208\pi$
$24$	4.36556	−	0.278018i	0.891117	−	0.0567501i
$25$			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	$0.0748452\pi$
$29$			2.50919i			0.465945i	−0.972483	+	0.232973i	$0.925155\pi$
$30$	−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
$33$	0.330172	−	0.0210267i	0.0574756	−	0.00366029i
$34$	−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
$39$	−1.94888	+	5.93312i	−0.312070	+	0.950059i
$40$	3.14057			0.496568
$41$	3.83398	−	3.83398i	0.598767	−	0.598767i	−0.341218	−	0.939984i	$-0.610839\pi$
$41$	3.83398	−	3.83398i	0.598767	−	0.598767i	0.939984	+	0.341218i	$0.110839\pi$
$42$	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
$45$	−2.95120	−	2.28195i	−0.439939	−	0.340173i
$46$	−1.14862	+	1.14862i	−0.169355	+	0.169355i
$47$	1.94994	+	1.94994i	0.284428	+	0.284428i	0.834872	−	0.550444i	$-0.185542\pi$
$47$	1.94994	+	1.94994i	0.284428	+	0.284428i	−0.550444	+	0.834872i	$0.685542\pi$
$48$	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	$-0.916988\pi$
$53$		−	3.75424i		−	0.515685i	0.966187	−	0.257843i	$-0.0830116\pi$
$54$	−7.82741	+	1.51182i	−1.06518	+	0.205733i
$55$	0.237524			0.0320278
$56$	−2.52557			−0.337493
$57$	−0.0703448	+	0.00447986i	−0.00931740	+	0.000593371i
$58$	2.72213	+	2.72213i	0.357433	+	0.357433i
$59$	−10.5526	−	10.5526i	−1.37384	−	1.37384i	−0.854679	−	0.519157i	$-0.826246\pi$
$59$	−10.5526	−	10.5526i	−1.37384	−	1.37384i	−0.519157	−	0.854679i	$-0.673754\pi$
$60$	−0.760592	+	0.0484377i	−0.0981920	+	0.00625328i
$61$	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
$63$	2.37328	+	1.83509i	0.299005	+	0.231199i
$64$			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	−0.992565	−	0.121714i	$-0.961161\pi$
$71$	−7.33792	+	7.33792i	−0.870851	+	0.870851i	0.121714	+	0.992565i	$0.461161\pi$
$72$	4.63463	−	5.99388i	0.546196	−	0.706385i
$73$	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
$78$	4.32235	+	8.55088i	0.489410	+	0.968196i
$79$	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	−0.127812	−	0.991798i	$-0.540795\pi$
$83$	7.87129	−	7.87129i	0.863987	−	0.863987i	0.991798	+	0.127812i	$0.0407953\pi$
$84$	0.611649	−	0.0389524i	0.0667363	−	0.00425005i
$85$	−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	0.0668438	−	0.997763i	$-0.478707\pi$
$89$	−8.78228	−	8.78228i	−0.930920	−	0.930920i	−0.997763	+	0.0668438i	$0.978707\pi$
$90$	−5.67725	+	0.726047i	−0.598434	+	0.0765321i
$91$	1.34062	−	3.34705i	0.140535	−	0.350866i
$92$			0.374648i			0.0390598i
$93$	0.145721	−	0.00928013i	0.0151106	−	0.000962305i
$94$	4.23083			0.436377
$95$	−0.0506058			−0.00519204
$96$	−0.217900	−	3.42157i	−0.0222394	−	0.349213i
$97$	−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
$99$	0.350522	−	0.453323i	0.0352287	−	0.0455607i
$100$	1.22209			0.122209
$101$	−5.88163			−0.585244			−0.292622	−	0.956228i	$-0.594528\pi$
$101$	−5.88163			−0.585244			−0.292622	+	0.956228i	$0.594528\pi$
$102$	0.539511	+	8.47165i	0.0534195	+	0.838819i
$103$			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	$0.291528\pi$
$107$			16.4075i			1.58618i	−0.609107	+	0.793088i	$0.708472\pi$
$108$	−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
$111$	−0.280659	−	4.40704i	−0.0266390	−	0.418298i
$112$	−3.24031	+	3.24031i	−0.306181	+	0.306181i
$113$		−	2.82075i		−	0.265354i	−0.991159	−	0.132677i	$-0.957643\pi$
$113$		−	2.82075i		−	0.265354i	0.991159	−	0.132677i	$-0.0423572\pi$
$114$	−0.0714544	+	0.0811744i	−0.00669232	+	0.00760268i
$115$	−0.930975	+	0.930975i	−0.0868139	+	0.0868139i
$116$	0.887880			0.0824376
$117$	5.48334	+	9.32379i	0.506935	+	0.861984i
$118$	−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
$123$	−0.596868	−	9.37230i	−0.0538178	−	0.845072i
$124$	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	$-0.898718\pi$
$131$		−	7.16133i		−	0.625688i	0.949804	−	0.312844i	$-0.101282\pi$
$132$	−0.00744034	−	0.116832i	−0.000647598	−	0.0101689i
$133$	0.0406959			0.00352878
$134$	13.5472			1.17030
$135$	−6.34422	+	1.22535i	−0.546024	+	0.105461i
$136$	−5.70480	−	5.70480i	−0.489183	−	0.489183i
$137$	−8.75820	−	8.75820i	−0.748264	−	0.748264i	0.225889	−	0.974153i	$-0.427471\pi$
$137$	−8.75820	−	8.75820i	−0.748264	−	0.748264i	−0.974153	+	0.225889i	$0.927471\pi$
$138$	0.178816	+	2.80785i	0.0152218	+	0.239020i
$139$	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
$141$	4.76671	−	0.303564i	0.401429	−	0.0255647i
$142$			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	−0.565336	−	0.824861i	$-0.691254\pi$
$149$	3.16790	−	3.16790i	0.259524	−	0.259524i	0.824861	+	0.565336i	$0.191254\pi$
$150$	9.15911	−	0.583291i	0.747838	−	0.0476255i
$151$	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
$156$	2.09944	+	0.689613i	0.168090	+	0.0552132i
$157$	−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
$162$	−6.99239	+	11.9067i	−0.549374	+	0.935475i
$163$	−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	0.613776	−	0.789480i	$-0.289650\pi$
$167$	−2.27059	−	2.27059i	−0.175703	−	0.175703i	−0.789480	+	0.613776i	$0.789650\pi$
$168$	−2.89033	+	3.28351i	−0.222994	+	0.253328i
$169$	8.97424	−	9.40548i	0.690326	−	0.723498i
$170$			6.09447i			0.467425i
$171$	−0.0746804	+	0.0965827i	−0.00571095	+	0.00738587i
$172$	1.63505			0.124672
$173$	19.7250			1.49967			0.749833	−	0.661627i	$-0.230134\pi$
$173$	19.7250			1.49967			0.749833	+	0.661627i	$0.230134\pi$
$174$	6.65434	−	0.423777i	0.504464	−	0.0321264i
$175$	−2.44212	−	2.44212i	−0.184607	−	0.184607i
$176$	0.618935	+	0.618935i	0.0466540	+	0.0466540i
$177$	−25.7963	+	1.64282i	−1.93897	+	0.123482i
$178$	−19.0551			−1.42824
$179$	−15.1369			−1.13139			−0.565694	−	0.824615i	$-0.691392\pi$
$179$	−15.1369			−1.13139			−0.565694	+	0.824615i	$0.691392\pi$
$180$	−0.807470	+	1.04429i	−0.0601852	+	0.0778364i
$181$		−	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
$189$	5.10186	−	0.985396i	0.371106	−	0.0716770i
$190$	−0.0549003	+	0.0549003i	−0.00398289	+	0.00398289i
$191$			22.6999i			1.64251i	0.570563	+	0.821254i	$0.306725\pi$
$191$			22.6999i			1.64251i	−0.570563	+	0.821254i	$0.693275\pi$
$192$	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
$195$	3.50332	+	6.93060i	0.250878	+	0.496311i
$196$	−0.353851			−0.0252751
$197$	−3.48543	+	3.48543i	−0.248327	+	0.248327i	−0.820284	−	0.571957i	$-0.806184\pi$
$197$	−3.48543	+	3.48543i	−0.248327	+	0.248327i	0.571957	+	0.820284i	$0.306184\pi$
$198$	−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
$201$	15.2631	−	0.972016i	1.07657	−	0.0685607i
$202$	−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
$210$	3.29777	−	0.210016i	0.227568	−	0.0144925i
$211$	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
$213$	1.14236	+	17.9378i	0.0782730	+	1.22908i
$214$	17.7999	+	17.7999i	1.21678	+	1.21678i
$215$	4.06300	+	4.06300i	0.277094	+	0.277094i
$216$	−2.48868	−	12.8851i	−0.169333	−	0.876719i
$217$	−0.0843025			−0.00572283
$218$	−24.8792			−1.68503
$219$	−0.0716276	−	1.12473i	−0.00484015	−	0.0760023i
$220$		−	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	−0.986771	−	0.162118i	$-0.948167\pi$
$227$	−12.4246	+	12.4246i	−0.824653	+	0.824653i	0.162118	+	0.986771i	$0.448167\pi$
$228$	0.00158520	+	0.0248916i	0.000104983	+	0.00164849i
$229$	−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	$-0.399855\pi$
$233$	9.44711			0.618901			0.309450	+	0.950916i	$0.399855\pi$
$234$	16.0637	+	4.16636i	1.05012	+	0.272363i
$235$	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	−0.445171	−	0.895445i	$-0.646857\pi$
$239$	6.96107	−	6.96107i	0.450274	−	0.450274i	0.895445	+	0.445171i	$0.146857\pi$
$240$	−0.627285	−	9.84993i	−0.0404911	−	0.635810i
$241$	−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
$249$	−1.22539	−	19.2417i	−0.0776560	−	1.21939i
$250$	16.1282			1.02003
$251$	7.20244			0.454614			0.227307	−	0.973823i	$-0.427008\pi$
$251$	7.20244			0.454614			0.227307	+	0.973823i	$0.427008\pi$
$252$	0.649347	−	0.839788i	0.0409050	−	0.0529017i
$253$	−0.143004	−	0.143004i	−0.00899056	−	0.00899056i
$254$	−12.2164	−	12.2164i	−0.766522	−	0.766522i
$255$	0.437281	+	6.86639i	0.0273836	+	0.429990i
$256$	8.24227			0.515142
$257$	−5.03844			−0.314289			−0.157145	−	0.987576i	$-0.550229\pi$
$257$	−5.03844			−0.314289			−0.157145	+	0.987576i	$0.550229\pi$
$258$	12.2541	−	0.780396i	0.762909	−	0.0485853i
$259$			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	$0.358194\pi$
$263$			29.2688i			1.80479i	−0.430907	+	0.902396i	$0.641806\pi$
$264$	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
$267$	−21.4686	+	1.36721i	−1.31386	+	0.0836720i
$268$	2.20935	−	2.20935i	0.134958	−	0.134958i
$269$			16.5644i			1.00995i	0.863135	+	0.504974i	$0.168498\pi$
$269$			16.5644i			1.00995i	−0.863135	+	0.504974i	$0.831502\pi$
$270$	−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
$273$	−2.81728	−	5.57341i	−0.170510	−	0.337318i
$274$	−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
$279$	0.154702	−	0.200073i	0.00926178	−	0.0119781i
$280$	−2.22072	+	2.22072i	−0.132713	+	0.132713i
$281$	6.72958	+	6.72958i	0.401453	+	0.401453i	0.878745	−	0.477292i	$-0.158381\pi$
$281$	6.72958	+	6.72958i	0.401453	+	0.401453i	−0.477292	+	0.878745i	$0.658381\pi$
$282$	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
$288$	−4.69779	−	3.63246i	−0.276820	−	0.214045i
$289$	−6.79545			−0.399732
$290$	4.78711			0.281108
$291$	−31.8638	+	2.02922i	−1.86789	+	0.118955i
$292$	−0.162807	−	0.162807i	−0.00952754	−	0.00952754i
$293$	11.5684	+	11.5684i	0.675834	+	0.675834i	0.959055	−	0.283221i	$-0.0914030\pi$
$293$	11.5684	+	11.5684i	0.675834	+	0.675834i	−0.283221	+	0.959055i	$0.591403\pi$
$294$	−2.65199	+	0.168890i	−0.154667	+	0.00984985i
$295$	−18.5578			−1.08047
$296$	6.43909			0.374264
$297$	−0.188222	−	0.974512i	−0.0109217	−	0.0565469i
$298$		−	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
$306$	11.6315	+	8.99379i	0.664928	+	0.514141i
$307$	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	$-0.622127\pi$
$311$	−13.2027			−0.748658			−0.374329	+	0.927296i	$0.622127\pi$
$312$	−14.0760	+	7.11523i	−0.796898	+	0.402821i
$313$	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	$-0.398861\pi$
$317$	22.4757	−	22.4757i	1.26236	−	1.26236i	0.949945	−	0.312419i	$-0.101139\pi$
$318$	−9.95620	+	0.634053i	−0.558316	+	0.0355559i
$319$	−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
$327$	−28.0304	+	1.78509i	−1.55008	+	0.0987158i
$328$	13.6938			0.756112
$329$	−2.75763			−0.152033
$330$	−0.0401154	−	0.629911i	−0.00220828	−	0.0346755i
$331$	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
$333$	−6.05083	−	4.67866i	−0.331583	−	0.256389i
$334$	−4.92655			−0.269569
$335$	10.9802			0.599911
$336$	0.504447	+	7.92106i	0.0275198	+	0.432129i
$337$		−	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
$345$	0.144933	+	2.27580i	0.00780292	+	0.122525i
$346$	21.3989	−	21.3989i	1.15041	−	1.15041i
$347$			22.8998i			1.22932i	0.788791	+	0.614662i	$0.210708\pi$
$347$			22.8998i			1.22932i	−0.788791	+	0.614662i	$0.789292\pi$
$348$	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
$351$	18.3972	+	3.54148i	0.981971	+	0.189030i
$352$	0.378097			0.0201526
$353$	3.69400	−	3.69400i	0.196612	−	0.196612i	−0.601934	−	0.798546i	$-0.705603\pi$
$353$	3.69400	−	3.69400i	0.196612	−	0.196612i	0.798546	+	0.601934i	$0.205603\pi$
$354$	−26.2032	+	29.7677i	−1.39268	+	1.58213i
$355$			12.9044i			0.684894i
$356$	−3.10762	+	3.10762i	−0.164703	+	0.164703i
$357$	−0.351650	−	5.52177i	−0.0186113	−	0.292243i
$358$	−16.4215	+	16.4215i	−0.867903	+	0.867903i
$359$	−21.5382	−	21.5382i	−1.13674	−	1.13674i	−0.989030	−	0.147714i	$-0.952809\pi$
$359$	−21.5382	−	21.5382i	−1.13674	−	1.13674i	−0.147714	−	0.989030i	$-0.547191\pi$
$360$	−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
$366$	−2.04113	−	32.0507i	−0.106691	−	1.67532i
$367$	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
$369$	−12.8681	−	9.94995i	−0.669885	−	0.517974i
$370$	−3.43946	−	3.43946i	−0.178809	−	0.178809i
$371$	2.65465	+	2.65465i	0.137823	+	0.137823i
$372$	−0.00328378	−	0.0515635i	−0.000170256	−	0.00267344i
$373$	−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
$375$	18.1709	−	1.15720i	0.938343	−	0.0597577i
$376$			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	−0.208682	−	0.977984i	$-0.566917\pi$
$383$	15.0555	−	15.0555i	0.769302	−	0.769302i	0.977984	+	0.208682i	$0.0669172\pi$
$384$	23.0947	−	1.47077i	1.17855	−	0.0750548i
$385$	−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	$-0.0709069\pi$
$389$	38.4715			1.95058			0.975291	+	0.220923i	$0.0709069\pi$
$390$	11.3194	+	3.71813i	0.573178	+	0.188275i
$391$	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
$396$	−0.160409	−	0.124032i	−0.00806084	−	0.00623286i
$397$	−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	0.310989	−	0.950413i	$-0.399340\pi$
$401$	−12.8045	−	12.8045i	−0.639424	−	0.639424i	−0.950413	+	0.310989i	$0.899340\pi$
$402$	15.5038	−	17.6128i	0.773260	−	0.878447i
$403$	−0.282165	−	0.113018i	−0.0140556	−	0.00562980i
$404$			2.08122i			0.103545i
$405$	−5.66743	+	9.65050i	−0.281617	+	0.479537i
$406$	−3.84967			−0.191056
$407$	0.486995			0.0241394
$408$	−13.9456	+	0.888115i	−0.690410	+	0.0439682i
$409$	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
$411$	−21.4098	+	1.36346i	−1.05607	+	0.0672547i
$412$	5.96664			0.293955
$413$	14.9237			0.734346
$414$	3.85516	+	2.98091i	0.189471	+	0.146504i
$415$		−	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	$-0.890150\pi$
$419$		−	13.8494i		−	0.676587i	0.941041	−	0.338294i	$-0.109850\pi$
$420$	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
$423$	5.06049	−	6.54464i	0.246050	−	0.318211i
$424$	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
$429$	−1.06458	+	0.538132i	−0.0513986	+	0.0259813i
$430$	8.81558			0.425125
$431$	3.37401	−	3.37401i	0.162521	−	0.162521i	−0.621162	−	0.783682i	$-0.713339\pi$
$431$	3.37401	−	3.37401i	0.162521	−	0.162521i	0.783682	+	0.621162i	$0.213339\pi$
$432$	−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
$435$	5.39343	−	0.343477i	0.258595	−	0.0164684i
$436$	−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	$-0.781820\pi$
$443$		−	26.6466i		−	1.26602i	0.774145	−	0.633009i	$-0.218180\pi$
$444$	−1.55944	+	0.0993115i	−0.0740076	+	0.00471312i
$445$	−15.4444			−0.732136
$446$	39.1388			1.85328
$447$	−0.493174	−	7.74405i	−0.0233263	−	0.366281i
$448$	−4.33319	−	4.33319i	−0.204724	−	0.204724i
$449$	7.80356	+	7.80356i	0.368273	+	0.368273i	0.866847	−	0.498574i	$-0.166143\pi$
$449$	7.80356	+	7.80356i	0.368273	+	0.368273i	−0.498574	+	0.866847i	$0.666143\pi$
$450$	9.72361	−	12.5754i	0.458376	−	0.592809i
$451$	1.03567			0.0487680
$452$	−0.998124			−0.0469478
$453$	−2.08861	−	32.7964i	−0.0981316	−	1.54091i
$454$			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	−0.824974	−	0.565171i	$-0.808810\pi$
$461$	−5.57821	+	5.57821i	−0.259803	+	0.259803i	0.565171	+	0.824974i	$0.308810\pi$
$462$	0.0322598	+	0.506559i	0.00150086	+	0.0235672i
$463$	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	$-0.697113\pi$
$467$	−25.0862			−1.16085			−0.580424	+	0.814314i	$0.697113\pi$
$468$	3.29923	−	1.94028i	0.152507	−	0.0896897i
$469$	−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
$474$	−1.06473	−	16.7188i	−0.0489045	−	0.767922i
$475$	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	0.627389	−	0.778706i	$-0.284123\pi$
$479$	−3.31172	−	3.31172i	−0.151316	−	0.151316i	−0.778706	+	0.627389i	$0.784123\pi$
$480$	−3.20017	−	2.81698i	−0.146067	−	0.128577i
$481$	−3.41799	+	8.53351i	−0.155847	+	0.389095i
$482$			25.6383i			1.16779i
$483$	−0.116551	−	1.83014i	−0.00530327	−	0.0832744i
$484$	−3.87945			−0.176339
$485$	−22.9227			−1.04087
$486$	7.47764	+	22.7172i	0.339193	+	1.03047i
$487$	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
$489$	0.696486	+	10.9365i	0.0314962	+	0.494568i
$490$	−1.90783			−0.0861869
$491$	8.65445			0.390570			0.195285	−	0.980747i	$-0.437437\pi$
$491$	8.65445			0.390570			0.195285	+	0.980747i	$0.437437\pi$
$492$	−3.31640	+	0.211202i	−0.149515	+	0.00952173i
$493$		−	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
$501$	−5.55054	+	0.353482i	−0.247980	+	0.0157924i
$502$	7.81366	−	7.81366i	0.348741	−	0.348741i
$503$			17.4205i			0.776742i	0.921503	+	0.388371i	$0.126962\pi$
$503$			17.4205i			0.776742i	−0.921503	+	0.388371i	$0.873038\pi$
$504$	0.961134	+	7.51549i	0.0428123	+	0.334766i
$505$	−5.17169	+	5.17169i	−0.230137	+	0.230137i
$506$	−0.310278			−0.0137936
$507$	−1.95776	−	22.4314i	−0.0869470	−	0.996213i
$508$	−3.98463			−0.176789
$509$	−16.6981	+	16.6981i	−0.740130	+	0.740130i	−0.972603	−	0.232473i	$-0.925318\pi$
$509$	−16.6981	+	16.6981i	−0.740130	+	0.740130i	0.232473	+	0.972603i	$0.425318\pi$
$510$	7.92347	+	6.97470i	0.350857	+	0.308845i
$511$			0.650679i			0.0287843i
$512$	−9.95321	+	9.95321i	−0.439874	+	0.439874i
$513$	0.0401016	+	0.207625i	0.00177053	+	0.00916686i
$514$	−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	$0.0675811\pi$
$521$			9.61958i			0.421442i	−0.977546	+	0.210721i	$0.932419\pi$
$522$	7.06447	−	9.13634i	0.309203	−	0.399887i
$523$	−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
$525$	−5.96985	+	0.380186i	−0.260546	+	0.0165927i
$526$	31.7526	+	31.7526i	1.38448	+	1.38448i
$527$	−0.190424	−	0.190424i	−0.00829501	−	0.00829501i
$528$	1.51301	−	0.0963549i	0.0658453	−	0.00419331i
$529$	−21.8790			−0.951261
$530$	−7.16245			−0.311117
$531$	−27.3862	+	35.4181i	−1.18846	+	1.53701i
$532$		−	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
$540$	0.433592	+	2.24491i	0.0186588	+	0.0966055i
$541$	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
$546$	−9.10274	−	2.99002i	−0.389562	−	0.127961i
$547$	−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
$552$	−4.62215	+	0.294358i	−0.196732	+	0.0125287i
$553$	−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	$-0.898354\pi$
$557$	−29.8168	−	29.8168i	−1.26338	−	1.26338i	−0.313932	−	0.949446i	$-0.601646\pi$
$558$	−0.0492215	−	0.384883i	−0.00208371	−	0.0162934i
$559$	−6.55572	−	15.3163i	−0.277278	−	0.647810i
$560$			5.69838i			0.240800i
$561$	−1.05472	+	0.0671690i	−0.0445303	+	0.00283588i
$562$	14.6013			0.615920
$563$	−31.4092			−1.32374			−0.661869	−	0.749620i	$-0.730237\pi$
$563$	−31.4092			−1.32374			−0.661869	+	0.749620i	$0.730237\pi$
$564$	−0.107416	−	1.68670i	−0.00452305	−	0.0710230i
$565$	−2.48027	−	2.48027i	−0.104346	−	0.104346i
$566$	29.8830	+	29.8830i	1.25608	+	1.25608i
$567$	4.55760	−	7.76069i	0.191401	−	0.325918i
$568$	−26.2088			−1.09970
$569$	−16.8044			−0.704478			−0.352239	−	0.935910i	$-0.614579\pi$
$569$	−16.8044			−0.704478			−0.352239	+	0.935910i	$0.614579\pi$
$570$	0.00854679	+	0.134206i	0.000357986	+	0.00562126i
$571$			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
$579$	−2.83820	−	44.5667i	−0.117952	−	1.85213i
$580$	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
$585$	13.0198	+	3.37689i	0.538304	+	0.139617i
$586$	25.1003			1.03688
$587$	3.68739	−	3.68739i	0.152195	−	0.152195i	−0.626903	−	0.779098i	$-0.715678\pi$
$587$	3.68739	−	3.68739i	0.152195	−	0.152195i	0.779098	+	0.626903i	$0.215678\pi$
$588$	−0.404957	+	0.460044i	−0.0167002	+	0.0189719i
$589$		−	0.00343076i		−	0.000141362i
$590$	−20.1326	+	20.1326i	−0.828847	+	0.828847i
$591$	0.542606	+	8.52026i	0.0223198	+	0.350477i
$592$	8.26137	−	8.26137i	0.339540	−	0.339540i
$593$	−6.58899	−	6.58899i	−0.270577	−	0.270577i	0.558755	−	0.829333i	$-0.311279\pi$
$593$	−6.58899	−	6.58899i	−0.270577	−	0.270577i	−0.829333	+	0.558755i	$0.811279\pi$
$594$	−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	$0.184594\pi$
$599$			26.8219i			1.09591i	−0.836507	+	0.547957i	$0.815406\pi$
$600$	0.960184	+	15.0773i	0.0391993	+	0.615527i
$601$	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
$603$	16.2038	−	20.9560i	0.659868	−	0.853395i
$604$	−4.74733	−	4.74733i	−0.193166	−	0.193166i
$605$	−9.64017	−	9.64017i	−0.391929	−	0.391929i
$606$	0.993346	+	15.5980i	0.0403519	+	0.633625i
$607$	−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
$609$	−4.33726	+	0.276215i	−0.175755	+	0.0111928i
$610$		−	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	−0.999967	−	0.00816772i	$-0.997400\pi$
$617$	−24.6358	+	24.6358i	−0.991799	+	0.991799i	0.00816772	+	0.999967i	$0.497400\pi$
$618$	44.7178	−	2.84782i	1.79881	−	0.114556i
$619$	−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
$624$	−8.93072	+	27.1885i	−0.357515	+	1.08841i
$625$	−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
$630$	3.50103	−	4.52781i	0.139484	−	0.180392i
$631$	−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
$639$	24.6285	+	19.0434i	0.974287	+	0.753345i
$640$	16.6142			0.656735
$641$	−9.53131			−0.376464			−0.188232	−	0.982125i	$-0.560276\pi$
$641$	−9.53131			−0.376464			−0.188232	+	0.982125i	$0.560276\pi$
$642$	43.5125	−	2.77106i	1.71730	−	0.109365i
$643$	−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
$645$	9.93215	−	0.632521i	0.391078	−	0.0249055i
$646$	0.199451			0.00784730
$647$	42.0485			1.65310			0.826548	−	0.562866i	$-0.190301\pi$
$647$	42.0485			1.65310			0.826548	+	0.562866i	$0.190301\pi$
$648$	−19.6001	−	11.5105i	−0.769966	−	0.452176i
$649$		−	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	$-0.984758\pi$
$653$		−	2.44638i		−	0.0957341i	0.998854	−	0.0478671i	$-0.0152424\pi$
$654$	−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
$657$	−1.54424	−	1.19405i	−0.0602467	−	0.0465844i
$658$	−2.99165	+	2.99165i	−0.116627	+	0.116627i
$659$		−	47.4472i		−	1.84828i	−0.382052	−	0.924141i	$-0.624783\pi$
$659$		−	47.4472i		−	1.84828i	0.382052	−	0.924141i	$-0.375217\pi$
$660$	−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
$663$	6.22561	−	18.9531i	0.241783	−	0.736077i
$664$	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
$669$	44.0961	−	2.80822i	1.70485	−	0.108572i
$670$	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	$0.158649\pi$
$677$			24.8760i			0.956061i	−0.878343	+	0.478031i	$0.841351\pi$
$678$	−7.48058	+	0.476395i	−0.287290	+	0.0182958i
$679$	18.4338			0.707426
$680$	−10.0324			−0.384725
$681$	1.93425	+	30.3725i	0.0741206	+	1.16388i
$682$	0.0174692	+	0.0174692i	0.000668931	+	0.000668931i
$683$	−20.7208	−	20.7208i	−0.792859	−	0.792859i	0.189099	−	0.981958i	$-0.439443\pi$
$683$	−20.7208	−	20.7208i	−0.792859	−	0.792859i	−0.981958	+	0.189099i	$0.939443\pi$
$684$	0.0341759	+	0.0264257i	0.00130675	+	0.00101041i
$685$	−15.4021			−0.588484
$686$	1.53423			0.0585770
$687$	0.529946	+	8.32146i	0.0202187	+	0.317484i
$688$			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
$696$	0.697599	+	10.9540i	0.0264424	+	0.415212i
$697$	−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	$-0.286199\pi$
$701$	32.9524			1.24460			0.622298	+	0.782780i	$0.286199\pi$
$702$	23.8005	−	16.1164i	0.898291	−	0.608275i
$703$	−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
$708$	0.581313	+	9.12805i	0.0218471	+	0.343053i
$709$	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
$717$	−1.08369	−	17.0166i	−0.0404711	−	0.635496i
$718$	−46.7320			−1.74402
$719$	21.3429			0.795954			0.397977	−	0.917395i	$-0.369712\pi$
$719$	21.3429			0.795954			0.397977	+	0.917395i	$0.369712\pi$
$720$	−13.5239	−	10.4570i	−0.504004	−	0.389710i
$721$	−11.9232	−	11.9232i	−0.444045	−	0.444045i
$722$	−20.6106	−	20.6106i	−0.767046	−	0.767046i
$723$	1.83955	+	28.8856i	0.0684138	+	1.07427i
$724$	−4.15230			−0.154319
$725$	−8.66594			−0.321845
$726$	−29.0751	+	1.85162i	−1.07908	+	0.0687202i
$727$		−	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
$735$	−2.14947	+	0.136887i	−0.0792844	+	0.00504917i
$736$	−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
$741$	0.226815	−	0.114652i	0.00833225	−	0.00421184i
$742$	5.75986			0.211451
$743$	−3.11030	+	3.11030i	−0.114106	+	0.114106i	−0.761854	−	0.647749i	$-0.775711\pi$
$743$	−3.11030	+	3.11030i	−0.114106	+	0.114106i	0.647749	+	0.761854i	$0.275711\pi$
$744$	0.276808	+	0.243662i	0.0101483	+	0.00893309i
$745$		−	5.57103i		−	0.204107i
$746$	−13.1023	+	13.1023i	−0.479711	+	0.479711i
$747$	−26.4186	−	20.4276i	−0.966607	−	0.747407i
$748$	−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
$756$	−0.348683	−	1.80530i	−0.0126815	−	0.0656581i
$757$	−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
$759$	−0.349578	+	0.0222626i	−0.0126889	+	0.000808080i
$760$	−0.0903740	−	0.0903740i	−0.00327821	−	0.00327821i
$761$	36.7325	+	36.7325i	1.33155	+	1.33155i	0.903981	+	0.427572i	$0.140631\pi$
$761$	36.7325	+	36.7325i	1.33155	+	1.33155i	0.427572	+	0.903981i	$0.359369\pi$
$762$	−29.8633	+	1.90182i	−1.08183	+	0.0688958i
$763$	16.2161			0.587063
$764$	8.03239			0.290602
$765$	9.42748	+	7.28959i	0.340851	+	0.263556i
$766$		−	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	−0.984696	−	0.174279i	$-0.944241\pi$
$773$	−22.5319	+	22.5319i	−0.810417	+	0.810417i	0.174279	+	0.984696i	$0.444241\pi$
$774$	13.0094	−	16.8248i	0.467613	−	0.604755i
$775$	−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
$780$	2.45240	−	1.23965i	0.0878100	−	0.0443867i
$781$	−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
$786$	−18.9918	+	1.20948i	−0.677413	+	0.0431405i
$787$	−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
$795$	−8.06964	+	0.513909i	−0.286201	+	0.0182265i
$796$	−0.230467			−0.00816867
$797$	−31.2383			−1.10652			−0.553259	−	0.833009i	$-0.686616\pi$
$797$	−31.2383			−1.10652			−0.553259	+	0.833009i	$0.686616\pi$
$798$	−0.00687311	−	0.107925i	−0.000243306	−	0.00382050i
$799$	−6.22900	−	6.22900i	−0.220366	−	0.220366i
$800$	4.83405	+	4.83405i	0.170910	+	0.170910i
$801$	−22.7918	+	29.4762i	−0.805308	+	1.04149i
$802$	−27.7821			−0.981021
$803$	0.124287			0.00438599
$804$	−0.343949	−	5.40085i	−0.0121301	−	0.190473i
$805$		−	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	$-0.840703\pi$
$809$		−	27.2948i		−	0.959634i	0.877369	−	0.479817i	$-0.159297\pi$
$810$	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
$813$	−1.25219	−	19.6626i	−0.0439164	−	0.689596i
$814$	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
$819$	−10.4702	−	2.71561i	−0.365859	−	0.0948910i
$820$	−2.38580			−0.0833159
$821$	−0.576885	+	0.576885i	−0.0201334	+	0.0201334i	−0.717102	−	0.696968i	$-0.754532\pi$
$821$	−0.576885	+	0.576885i	−0.0201334	+	0.0201334i	0.696968	+	0.717102i	$0.254532\pi$
$822$	−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
$825$	0.0726197	+	1.14031i	0.00252829	+	0.0397004i
$826$	16.1901	−	16.1901i	0.563327	−	0.563327i
$827$	11.1442	+	11.1442i	0.387520	+	0.387520i	0.873802	−	0.486282i	$-0.161647\pi$
$827$	11.1442	+	11.1442i	0.387520	+	0.387520i	−0.486282	+	0.873802i	$0.661647\pi$
$828$	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
$834$	−0.417444	−	6.55490i	−0.0144549	−	0.226978i
$835$	−3.99304			−0.138185
$836$	−0.00275061			−9.51319e−5
$837$	−0.0830713	−	0.430100i	−0.00287137	−	0.0148664i
$838$	−15.0247	−	15.0247i	−0.519019	−	0.519019i
$839$	−17.7174	−	17.7174i	−0.611673	−	0.611673i	0.331709	−	0.943382i	$-0.392375\pi$
$839$	−17.7174	−	17.7174i	−0.611673	−	0.611673i	−0.943382	+	0.331709i	$0.892375\pi$
$840$	0.345718	+	5.42863i	0.0119284	+	0.187305i
$841$	22.7040			0.782895
$842$	0.429408			0.0147984
$843$	16.4507	−	1.04765i	0.566593	−	0.0360830i
$844$		−	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
$852$	6.34732	−	0.404224i	0.217455	−	0.0138485i
$853$	−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	$-0.156228\pi$
$857$	51.6376			1.76391			0.881954	+	0.471336i	$0.156228\pi$
$858$	−0.571127	+	1.73872i	−0.0194980	+	0.0593591i
$859$	−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	−0.491289	−	0.870996i	$-0.663474\pi$
$863$	11.1546	−	11.1546i	0.379707	−	0.379707i	0.870996	+	0.491289i	$0.163474\pi$
$864$	−10.0989	+	1.95054i	−0.343571	+	0.0663588i
$865$	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
$873$	−33.8277	+	43.7487i	−1.14489	+	1.48067i
$874$	0.0661064			0.00223608
$875$	−10.5122			−0.355379
$876$	−0.397987	+	0.0253455i	−0.0134467	+	0.000856345i
$877$	−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
$879$	28.2794	−	1.80095i	0.953841	−	0.0607446i
$880$	1.08845			0.0366918
$881$	26.0001			0.875965			0.437983	−	0.898983i	$-0.355693\pi$
$881$	26.0001			0.875965			0.437983	+	0.898983i	$0.355693\pi$
$882$	−2.81544	+	3.64115i	−0.0948007	+	0.122604i
$883$		−	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	$0.206262\pi$
$887$			35.9526i			1.20717i	−0.797298	+	0.603586i	$0.793738\pi$
$888$	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
$891$	−1.48238	−	0.870552i	−0.0496615	−	0.0291646i
$892$	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
$897$	2.06342	−	6.28183i	0.0688957	−	0.209744i
$898$	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
$903$	−7.98718	+	0.508657i	−0.265797	+	0.0169271i
$904$	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	$-0.825089\pi$
$911$		−	31.5266i		−	1.04452i	0.852785	−	0.522261i	$-0.174911\pi$
$912$	−0.322355	+	0.0205289i	−0.0106742	+	0.000679780i
$913$	2.12628			0.0703695
$914$	23.3722			0.773085
$915$	−1.65436	−	25.9776i	−0.0546915	−	0.858792i
$916$	1.20455	+	1.20455i	0.0397993	+	0.0397993i
$917$	5.06383	+	5.06383i	0.167222	+	0.167222i
$918$	25.0043	−	4.82945i	0.825266	−	0.159395i
$919$	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
$921$	−0.116169	−	1.82414i	−0.00382790	−	0.0601076i
$922$			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	−0.925385	−	0.379029i	$-0.876258\pi$
$929$	−16.6527	+	16.6527i	−0.546356	+	0.546356i	0.379029	+	0.925385i	$0.376258\pi$
$930$	−0.0177049	−	0.278011i	−0.000580566	−	0.00911633i
$931$	−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
$936$	−6.85844	+	26.4432i	−0.224175	+	0.864324i
$937$	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	−0.854193	−	0.519957i	$-0.825948\pi$
$941$	−10.2529	+	10.2529i	−0.334236	+	0.334236i	0.519957	+	0.854193i	$0.325948\pi$
$942$	3.14864	+	49.4414i	0.102588	+	1.61089i
$943$	−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	0.999445	−	0.0333124i	$-0.0106056\pi$
$947$	29.7312	+	29.7312i	0.966133	+	0.966133i	−0.0333124	+	0.999445i	$0.510606\pi$
$948$	−2.90025	−	2.55296i	−0.0941956	−	0.0829164i
$949$	−0.872313	+	2.17785i	−0.0283165	+	0.0706962i
$950$		−	0.215636i		−	0.00699617i
$951$	−3.49899	−	54.9428i	−0.113462	−	1.78164i
$952$	8.06781			0.261479
$953$	−39.8792			−1.29181			−0.645907	−	0.763416i	$-0.723521\pi$
$953$	−39.8792			−1.29181			−0.645907	+	0.763416i	$0.723521\pi$
$954$	−10.5698	+	13.6698i	−0.342211	+	0.442575i
$955$	19.9599	+	19.9599i	0.645888	+	0.645888i
$956$	−2.46318	−	2.46318i	−0.0796649	−	0.0796649i
$957$	0.0527601	+	0.828465i	0.00170549	+	0.0267805i
$958$	−7.18552			−0.232154
$959$	12.3860			0.399964
$960$	13.1721	−	0.838854i	0.425127	−	0.0270739i
$961$		−	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
$969$	0.224713	−	0.0143107i	0.00721884	−	0.000459726i
$970$	−24.8679	+	24.8679i	−0.798462	+	0.798462i
$971$		−	47.3579i		−	1.51979i	−0.650047	−	0.759894i	$-0.725251\pi$
$971$		−	47.3579i		−	1.51979i	0.650047	−	0.759894i	$-0.274749\pi$
$972$	4.92434	+	2.48535i	0.157948	+	0.0797177i
$973$	−1.74775	+	1.74775i	−0.0560303	+	0.0560303i
$974$	51.6294			1.65431
$975$	−20.4911	−	6.73080i	−0.656240	−	0.215558i
$976$	55.3820			1.77273
$977$	−5.65121	+	5.65121i	−0.180798	+	0.180798i	−0.791704	−	0.610905i	$-0.790806\pi$
$977$	−5.65121	+	5.65121i	−0.180798	+	0.180798i	0.610905	+	0.791704i	$0.290806\pi$
$978$	12.6202	+	11.1091i	0.403551	+	0.355228i
$979$		−	2.37236i		−	0.0758210i
$980$	−0.311139	+	0.311139i	−0.00993899	+	0.00993899i
$981$	−29.7580	+	38.4854i	−0.950099	+	1.22874i
$982$	9.38889	−	9.38889i	0.299611	−	0.299611i
$983$	5.63320	+	5.63320i	0.179671	+	0.179671i	0.791213	−	0.611541i	$-0.209450\pi$
$983$	5.63320	+	5.63320i	0.179671	+	0.179671i	−0.611541	+	0.791213i	$0.709450\pi$
$984$	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
$990$	−0.864862	−	0.668735i	−0.0274871	−	0.0212538i
$991$	−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
$993$	24.7987	−	1.57929i	0.786964	−	0.0501172i
$994$	−11.2580	−	11.2580i	−0.357083	−	0.357083i
$995$	−0.572694	−	0.572694i	−0.0181556	−	0.0181556i
$996$	−6.80869	+	0.433606i	−0.215741	+	0.0137393i
$997$	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
$999$	−13.0075	+	2.51233i	−0.411540	+	0.0794866i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.08486 - 1.08486i) q^{2} +(1.14443 - 1.30011i) q^{3} -0.353851i q^{4} +(0.879295 - 0.879295i) q^{5} +(-0.168890 - 2.65199i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.78584 + 1.78584i) q^{8} +(-0.380562 - 2.97576i) q^{9} +O(q^{10})\)	\(q+(1.08486 - 1.08486i) q^{2} +(1.14443 - 1.30011i) q^{3} -0.353851i q^{4} +(0.879295 - 0.879295i) q^{5} +(-0.168890 - 2.65199i) 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} +(-0.136887 - 2.14947i) q^{15} +4.58249 q^{16} -3.19446 q^{17} +(-3.64115 - 2.81544i) q^{18} +(-0.0287763 - 0.0287763i) q^{19} +(-0.311139 - 0.311139i) q^{20} +(0.110081 + 1.72855i) q^{21} +0.293054 q^{22} -1.05877 q^{23} +(4.36556 - 0.278018i) 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} +(0.330172 - 0.0210267i) 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} +(-1.94888 + 5.93312i) 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} +(-2.95120 - 2.28195i) 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} +(-7.82741 + 1.51182i) q^{54} +0.237524 q^{55} -2.52557 q^{56} +(-0.0703448 + 0.00447986i) q^{57} +(2.72213 + 2.72213i) q^{58} +(-10.5526 - 10.5526i) q^{59} +(-0.760592 + 0.0484377i) q^{60} +12.0856 q^{61} +0.129339 q^{62} +(2.37328 + 1.83509i) 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} +(4.63463 - 5.99388i) 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} +(4.32235 + 8.55088i) 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} +(0.611649 - 0.0389524i) 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} +(0.145721 - 0.00928013i) q^{93} +4.23083 q^{94} -0.0506058 q^{95} +(-0.217900 - 3.42157i) q^{96} +(-13.0347 - 13.0347i) q^{97} +(-1.08486 - 1.08486i) q^{98} +(0.350522 - 0.453323i) 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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