LMFDB - Embedded newform 546.2.by.b.115.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.8
Character	$\chi$	$=$	546.115
Dual form			546.2.by.b.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.45998 - 0.391201i) q^{5} +(0.258819 + 0.965926i) q^{6} +(0.541277 + 2.58979i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.45998 - 0.391201i) q^{5} +(0.258819 + 0.965926i) q^{6} +(0.541277 + 2.58979i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -1.51148 q^{10} +(-4.40060 + 4.40060i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.30092 + 2.77593i) q^{13} +(1.19312 + 2.36145i) q^{14} +(0.391201 - 1.45998i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.75313 + 6.50061i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(5.46599 - 5.46599i) q^{19} +(-1.45998 + 0.391201i) q^{20} +(-2.58979 + 0.541277i) q^{21} +(-3.11170 + 5.38962i) q^{22} +(-0.0523450 - 0.0302214i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-2.35162 - 1.35771i) q^{25} +(2.94098 + 2.08582i) q^{26} -1.00000i q^{27} +(1.76365 + 1.97219i) q^{28} +(1.60863 + 2.78623i) q^{29} -1.51148i q^{30} +(-2.10867 - 7.86967i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-4.40060 - 4.40060i) q^{33} +(5.30773 + 5.30773i) q^{34} +(0.222875 - 3.99280i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(1.25023 + 4.66593i) q^{37} +(3.86504 - 6.69444i) q^{38} +(-2.77593 + 2.30092i) q^{39} +(-1.30898 + 0.755742i) q^{40} +(-3.84810 - 1.03109i) q^{41} +(-2.36145 + 1.19312i) q^{42} +(3.84700 + 2.22107i) q^{43} +(-1.61073 + 6.01134i) q^{44} +(1.45998 + 0.391201i) q^{45} +(-0.0583833 - 0.0156437i) q^{46} +(0.335258 - 1.25120i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-6.41404 + 2.80359i) q^{49} +(-2.62289 - 0.702801i) q^{50} +(-6.50061 + 3.75313i) q^{51} +(3.38062 + 1.25357i) q^{52} +(-1.81627 + 3.14587i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(8.14632 - 4.70328i) q^{55} +(2.21400 + 1.44852i) q^{56} +(5.46599 + 5.46599i) q^{57} +(2.27495 + 2.27495i) q^{58} +(2.57637 - 9.61514i) q^{59} +(-0.391201 - 1.45998i) q^{60} -0.829226i q^{61} +(-4.07364 - 7.05576i) q^{62} +(-0.541277 - 2.58979i) q^{63} -1.00000i q^{64} +(-2.27335 - 4.95293i) q^{65} +(-5.38962 - 3.11170i) q^{66} +(-0.615467 - 0.615467i) q^{67} +(6.50061 + 3.75313i) q^{68} +(0.0302214 - 0.0523450i) q^{69} +(-0.818131 - 3.91443i) q^{70} +(-0.497499 + 0.133304i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(7.87352 - 2.10970i) q^{73} +(2.41526 + 4.18336i) q^{74} +(1.35771 - 2.35162i) q^{75} +(2.00069 - 7.46668i) q^{76} +(-13.7786 - 9.01470i) q^{77} +(-2.08582 + 2.94098i) q^{78} +(-5.73437 - 9.93222i) q^{79} +(-1.06878 + 1.06878i) q^{80} +1.00000 q^{81} -3.98384 q^{82} +(4.74859 - 4.74859i) q^{83} +(-1.97219 + 1.76365i) q^{84} +(-2.93646 - 10.9590i) q^{85} +(4.29077 + 1.14971i) q^{86} +(-2.78623 + 1.60863i) q^{87} +6.22339i q^{88} +(-2.77244 + 0.742873i) q^{89} +1.51148 q^{90} +(-5.94364 + 7.46144i) q^{91} -0.0604428 q^{92} +(7.86967 - 2.10867i) q^{93} -1.29534i q^{94} +(-10.1185 + 5.84194i) q^{95} +(0.965926 + 0.258819i) q^{96} +(-0.663690 - 2.47693i) q^{97} +(-5.46986 + 4.36813i) q^{98} +(4.40060 - 4.40060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.45998	−	0.391201i	−0.652924	−	0.174950i	−0.0828733	−	0.996560i	$-0.526410\pi$
$5$	−1.45998	−	0.391201i	−0.652924	−	0.174950i	−0.570050	+	0.821610i	$0.693076\pi$
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	0.541277	+	2.58979i	0.204583	+	0.978849i
$7$	0.541277	+	2.58979i	0.204583	+	0.978849i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−1.51148			−0.477973
$11$	−4.40060	+	4.40060i	−1.32683	+	1.32683i	−0.418714	+	0.908118i	$0.637519\pi$
$11$	−4.40060	+	4.40060i	−1.32683	+	1.32683i	−0.908118	+	0.418714i	$0.862481\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	2.30092	+	2.77593i	0.638160	+	0.769904i
$13$	2.30092	+	2.77593i	0.638160	+	0.769904i
$14$	1.19312	+	2.36145i	0.318875	+	0.631125i
$15$	0.391201	−	1.45998i	0.101008	−	0.376966i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.75313	+	6.50061i	0.910268	+	1.57663i	0.813686	+	0.581305i	$0.197458\pi$
$17$	3.75313	+	6.50061i	0.910268	+	1.57663i	0.0965823	+	0.995325i	$0.469209\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	5.46599	−	5.46599i	1.25398	−	1.25398i	0.300065	−	0.953919i	$-0.402992\pi$
$19$	5.46599	−	5.46599i	1.25398	−	1.25398i	0.953919	−	0.300065i	$-0.0970083\pi$
$20$	−1.45998	+	0.391201i	−0.326462	+	0.0874752i
$21$	−2.58979	+	0.541277i	−0.565139	+	0.118116i
$22$	−3.11170	+	5.38962i	−0.663416	+	1.14907i
$23$	−0.0523450	−	0.0302214i	−0.0109147	−	0.00630160i	0.494533	−	0.869159i	$-0.335339\pi$
$23$	−0.0523450	−	0.0302214i	−0.0109147	−	0.00630160i	−0.505447	+	0.862857i	$0.668673\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−2.35162	−	1.35771i	−0.470324	−	0.271542i
$26$	2.94098	+	2.08582i	0.576773	+	0.409063i
$27$		−	1.00000i		−	0.192450i
$28$	1.76365	+	1.97219i	0.333299	+	0.372708i
$29$	1.60863	+	2.78623i	0.298716	+	0.517391i	0.975842	−	0.218476i	$-0.0701085\pi$
$29$	1.60863	+	2.78623i	0.298716	+	0.517391i	−0.677127	+	0.735866i	$0.736775\pi$
$30$		−	1.51148i		−	0.275958i
$31$	−2.10867	−	7.86967i	−0.378729	−	1.41344i	−0.847819	−	0.530285i	$-0.822085\pi$
$31$	−2.10867	−	7.86967i	−0.378729	−	1.41344i	0.469091	−	0.883150i	$-0.344582\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−4.40060	−	4.40060i	−0.766047	−	0.766047i
$34$	5.30773	+	5.30773i	0.910268	+	0.910268i
$35$	0.222875	−	3.99280i	0.0376727	−	0.674906i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	1.25023	+	4.66593i	0.205537	+	0.767074i	0.989285	+	0.145996i	$0.0466386\pi$
$37$	1.25023	+	4.66593i	0.205537	+	0.767074i	−0.783748	+	0.621079i	$0.786695\pi$
$38$	3.86504	−	6.69444i	0.626992	−	1.08598i
$39$	−2.77593	+	2.30092i	−0.444504	+	0.368442i
$40$	−1.30898	+	0.755742i	−0.206969	+	0.119493i
$41$	−3.84810	−	1.03109i	−0.600972	−	0.161030i	−0.0545089	−	0.998513i	$-0.517359\pi$
$41$	−3.84810	−	1.03109i	−0.600972	−	0.161030i	−0.546463	+	0.837483i	$0.684026\pi$
$42$	−2.36145	+	1.19312i	−0.364380	+	0.184102i
$43$	3.84700	+	2.22107i	0.586662	+	0.338709i	0.763777	−	0.645481i	$-0.223343\pi$
$43$	3.84700	+	2.22107i	0.586662	+	0.338709i	−0.177114	+	0.984190i	$0.556676\pi$
$44$	−1.61073	+	6.01134i	−0.242827	+	0.906243i
$45$	1.45998	+	0.391201i	0.217641	+	0.0583168i
$46$	−0.0583833	−	0.0156437i	−0.00860814	−	0.00230654i
$47$	0.335258	−	1.25120i	0.0489024	−	0.182506i	−0.937155	−	0.348915i	$-0.886550\pi$
$47$	0.335258	−	1.25120i	0.0489024	−	0.182506i	0.986057	+	0.166408i	$0.0532170\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−6.41404	+	2.80359i	−0.916291	+	0.400512i
$50$	−2.62289	−	0.702801i	−0.370933	−	0.0993911i
$51$	−6.50061	+	3.75313i	−0.910268	+	0.525543i
$52$	3.38062	+	1.25357i	0.468807	+	0.173838i
$53$	−1.81627	+	3.14587i	−0.249484	+	0.432119i	−0.963383	−	0.268130i	$-0.913594\pi$
$53$	−1.81627	+	3.14587i	−0.249484	+	0.432119i	0.713899	+	0.700249i	$0.246928\pi$
$54$	−0.258819	−	0.965926i	−0.0352208	−	0.131446i
$55$	8.14632	−	4.70328i	1.09845	−	0.634190i
$56$	2.21400	+	1.44852i	0.295858	+	0.193566i
$57$	5.46599	+	5.46599i	0.723988	+	0.723988i
$58$	2.27495	+	2.27495i	0.298716	+	0.298716i
$59$	2.57637	−	9.61514i	0.335415	−	1.25178i	−0.568005	−	0.823025i	$-0.692284\pi$
$59$	2.57637	−	9.61514i	0.335415	−	1.25178i	0.903419	−	0.428759i	$-0.141049\pi$
$60$	−0.391201	−	1.45998i	−0.0505038	−	0.188483i
$61$		−	0.829226i		−	0.106172i	−0.998590	−	0.0530858i	$-0.983094\pi$
$61$		−	0.829226i		−	0.106172i	0.998590	−	0.0530858i	$-0.0169057\pi$
$62$	−4.07364	−	7.05576i	−0.517353	−	0.896082i
$63$	−0.541277	−	2.58979i	−0.0681944	−	0.326283i
$64$		−	1.00000i		−	0.125000i
$65$	−2.27335	−	4.95293i	−0.281975	−	0.614335i
$66$	−5.38962	−	3.11170i	−0.663416	−	0.383023i
$67$	−0.615467	−	0.615467i	−0.0751913	−	0.0751913i	0.668511	−	0.743702i	$-0.266932\pi$
$67$	−0.615467	−	0.615467i	−0.0751913	−	0.0751913i	−0.743702	+	0.668511i	$0.766932\pi$
$68$	6.50061	+	3.75313i	0.788315	+	0.455134i
$69$	0.0302214	−	0.0523450i	0.00363823	−	0.00630160i
$70$	−0.818131	−	3.91443i	−0.0977854	−	0.467864i
$71$	−0.497499	+	0.133304i	−0.0590423	+	0.0158203i	−0.288219	−	0.957564i	$-0.593063\pi$
$71$	−0.497499	+	0.133304i	−0.0590423	+	0.0158203i	0.229177	+	0.973385i	$0.426397\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	7.87352	−	2.10970i	0.921525	−	0.246922i	0.233288	−	0.972408i	$-0.425051\pi$
$73$	7.87352	−	2.10970i	0.921525	−	0.246922i	0.688237	+	0.725486i	$0.258385\pi$
$74$	2.41526	+	4.18336i	0.280769	+	0.486306i
$75$	1.35771	−	2.35162i	0.156775	−	0.271542i
$76$	2.00069	−	7.46668i	0.229495	−	0.856487i
$77$	−13.7786	−	9.01470i	−1.57022	−	1.02732i
$78$	−2.08582	+	2.94098i	−0.236173	+	0.333000i
$79$	−5.73437	−	9.93222i	−0.645167	−	1.11746i	−0.984263	−	0.176711i	$-0.943454\pi$
$79$	−5.73437	−	9.93222i	−0.645167	−	1.11746i	0.339096	−	0.940752i	$-0.389879\pi$
$80$	−1.06878	+	1.06878i	−0.119493	+	0.119493i
$81$	1.00000			0.111111
$82$	−3.98384			−0.439942
$83$	4.74859	−	4.74859i	0.521226	−	0.521226i	−0.396716	−	0.917942i	$-0.629850\pi$
$83$	4.74859	−	4.74859i	0.521226	−	0.521226i	0.917942	+	0.396716i	$0.129850\pi$
$84$	−1.97219	+	1.76365i	−0.215183	+	0.192431i
$85$	−2.93646	−	10.9590i	−0.318503	−	1.18867i
$86$	4.29077	+	1.14971i	0.462686	+	0.123976i
$87$	−2.78623	+	1.60863i	−0.298716	+	0.172464i
$88$			6.22339i			0.663416i
$89$	−2.77244	+	0.742873i	−0.293878	+	0.0787443i	−0.402746	−	0.915312i	$-0.631944\pi$
$89$	−2.77244	+	0.742873i	−0.293878	+	0.0787443i	0.108868	+	0.994056i	$0.465277\pi$
$90$	1.51148			0.159324
$91$	−5.94364	+	7.46144i	−0.623063	+	0.782172i
$92$	−0.0604428			−0.00630160
$93$	7.86967	−	2.10867i	0.816047	−	0.218659i
$94$		−	1.29534i		−	0.133604i
$95$	−10.1185	+	5.84194i	−1.03814	+	0.599371i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	−0.663690	−	2.47693i	−0.0673876	−	0.251494i	0.924012	−	0.382363i	$-0.124890\pi$
$97$	−0.663690	−	2.47693i	−0.0673876	−	0.251494i	−0.991400	+	0.130870i	$0.958223\pi$
$98$	−5.46986	+	4.36813i	−0.552540	+	0.441248i
$99$	4.40060	−	4.40060i	0.442277	−	0.442277i
$100$	−2.71542			−0.271542
$101$	8.05624			0.801626			0.400813	−	0.916160i	$-0.368728\pi$
$101$	8.05624			0.801626			0.400813	+	0.916160i	$0.368728\pi$
$102$	−5.30773	+	5.30773i	−0.525543	+	0.525543i
$103$	6.92712	+	11.9981i	0.682549	+	1.18221i	0.974200	+	0.225685i	$0.0724620\pi$
$103$	6.92712	+	11.9981i	0.682549	+	1.18221i	−0.291651	+	0.956525i	$0.594205\pi$
$104$	3.58987	+	0.335884i	0.352016	+	0.0329361i
$105$	3.99280	+	0.222875i	0.389657	+	0.0217504i
$106$	−0.940170	+	3.50876i	−0.0913174	+	0.340801i
$107$	5.18435	−	8.97955i	0.501190	−	0.868086i	−0.498809	−	0.866712i	$-0.666229\pi$
$107$	5.18435	−	8.97955i	0.501190	−	0.868086i	0.999999	−	0.00137430i	$-0.000437454\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	13.5916	−	3.64186i	1.30184	−	0.348827i	0.459693	−	0.888078i	$-0.347959\pi$
$109$	13.5916	−	3.64186i	1.30184	−	0.348827i	0.842145	+	0.539251i	$0.181293\pi$
$110$	6.65144	−	6.65144i	0.634190	−	0.634190i
$111$	−4.66593	+	1.25023i	−0.442871	+	0.118667i
$112$	2.51346	+	0.826136i	0.237500	+	0.0780626i
$113$	−5.52604	+	9.57138i	−0.519846	+	0.900400i	0.479888	+	0.877330i	$0.340677\pi$
$113$	−5.52604	+	9.57138i	−0.519846	+	0.900400i	−0.999734	+	0.0230698i	$0.992656\pi$
$114$	6.69444	+	3.86504i	0.626992	+	0.361994i
$115$	0.0646001	+	0.0646001i	0.00602399	+	0.00602399i
$116$	2.78623	+	1.60863i	0.258695	+	0.149358i
$117$	−2.30092	−	2.77593i	−0.212720	−	0.256635i
$118$		−	9.95432i		−	0.916370i
$119$	−14.8038	+	13.2385i	−1.35706	+	1.21357i
$120$	−0.755742	−	1.30898i	−0.0689895	−	0.119493i
$121$		−	27.7306i		−	2.52097i
$122$	−0.214619	−	0.800971i	−0.0194307	−	0.0725165i
$123$	1.03109	−	3.84810i	0.0929706	−	0.346971i
$124$	−5.76100	−	5.76100i	−0.517353	−	0.517353i
$125$	8.24609	+	8.24609i	0.737553	+	0.737553i
$126$	−1.19312	−	2.36145i	−0.106292	−	0.210375i
$127$	−5.30387	+	3.06219i	−0.470643	+	0.271726i	−0.716509	−	0.697578i	$-0.754261\pi$
$127$	−5.30387	+	3.06219i	−0.470643	+	0.271726i	0.245866	+	0.969304i	$0.420928\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−2.22107	+	3.84700i	−0.195554	+	0.338709i
$130$	−3.47780	−	4.19577i	−0.305023	−	0.367994i
$131$	10.0027	−	5.77506i	0.873939	−	0.504569i	0.00528386	−	0.999986i	$-0.498318\pi$
$131$	10.0027	−	5.77506i	0.873939	−	0.504569i	0.868655	+	0.495417i	$0.164985\pi$
$132$	−6.01134	−	1.61073i	−0.523220	−	0.140196i
$133$	17.1144	+	11.1972i	1.48400	+	0.970917i
$134$	−0.753791	−	0.435201i	−0.0651176	−	0.0375957i
$135$	−0.391201	+	1.45998i	−0.0336692	+	0.125655i
$136$	7.25049	+	1.94276i	0.621725	+	0.166591i
$137$	4.10069	+	1.09878i	0.350346	+	0.0938749i	0.429700	−	0.902972i	$-0.358619\pi$
$137$	4.10069	+	1.09878i	0.350346	+	0.0938749i	−0.0793545	+	0.996846i	$0.525286\pi$
$138$	0.0156437	−	0.0583833i	0.00133168	−	0.00496991i
$139$	7.54445	+	4.35579i	0.639912	+	0.369454i	0.784581	−	0.620027i	$-0.212878\pi$
$139$	7.54445	+	4.35579i	0.639912	+	0.369454i	−0.144668	+	0.989480i	$0.546212\pi$
$140$	−1.80338	−	3.56930i	−0.152414	−	0.301661i
$141$	1.25120	+	0.335258i	0.105370	+	0.0282338i
$142$	−0.446045	+	0.257524i	−0.0374313	+	0.0216110i
$143$	−22.3412	−	2.09034i	−1.86826	−	0.174803i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.25860	−	4.69715i	−0.104521	−	0.390077i
$146$	7.05920	−	4.07563i	0.584224	−	0.337302i
$147$	−2.80359	−	6.41404i	−0.231236	−	0.529021i
$148$	3.41570	+	3.41570i	0.280769	+	0.280769i
$149$	−3.84805	−	3.84805i	−0.315245	−	0.315245i	0.531693	−	0.846937i	$-0.321556\pi$
$149$	−3.84805	−	3.84805i	−0.315245	−	0.315245i	−0.846937	+	0.531693i	$0.821556\pi$
$150$	0.702801	−	2.62289i	0.0573835	−	0.214158i
$151$	−3.54781	−	13.2406i	−0.288717	−	1.07751i	−0.946080	−	0.323932i	$-0.894995\pi$
$151$	−3.54781	−	13.2406i	−0.288717	−	1.07751i	0.657363	−	0.753574i	$-0.271672\pi$
$152$		−	7.73007i		−	0.626992i
$153$	−3.75313	−	6.50061i	−0.303423	−	0.525543i
$154$	−15.6423	−	5.14137i	−1.26049	−	0.414304i
$155$			12.3145i			0.989124i
$156$	−1.25357	+	3.38062i	−0.100366	+	0.270666i
$157$	19.3289	+	11.1595i	1.54261	+	0.890628i	0.998673	+	0.0515038i	$0.0164014\pi$
$157$	19.3289	+	11.1595i	1.54261	+	0.890628i	0.543940	+	0.839124i	$0.316932\pi$
$158$	−8.10963	−	8.10963i	−0.645167	−	0.645167i
$159$	−3.14587	−	1.81627i	−0.249484	−	0.144040i
$160$	−0.755742	+	1.30898i	−0.0597467	+	0.103484i
$161$	0.0499340	−	0.151921i	0.00393535	−	0.0119730i
$162$	0.965926	−	0.258819i	0.0758903	−	0.0203347i
$163$	−8.34888	+	8.34888i	−0.653935	+	0.653935i	−0.953938	−	0.300003i	$-0.903012\pi$
$163$	−8.34888	+	8.34888i	−0.653935	+	0.653935i	0.300003	+	0.953938i	$0.403012\pi$
$164$	−3.84810	+	1.03109i	−0.300486	+	0.0805149i
$165$	4.70328	+	8.14632i	0.366150	+	0.634190i
$166$	3.35776	−	5.81582i	0.260613	−	0.451395i
$167$	2.31131	−	8.62592i	0.178854	−	0.667493i	−0.817009	−	0.576625i	$-0.804369\pi$
$167$	2.31131	−	8.62592i	0.178854	−	0.667493i	0.995863	−	0.0908680i	$-0.0289641\pi$
$168$	−1.44852	+	2.21400i	−0.111756	+	0.170814i
$169$	−2.41156	+	12.7744i	−0.185504	+	0.982643i
$170$	−5.67280	−	9.82558i	−0.435084	−	0.753587i
$171$	−5.46599	+	5.46599i	−0.417995	+	0.417995i
$172$	4.44213			0.338709
$173$	−22.1636			−1.68507			−0.842533	−	0.538645i	$-0.818937\pi$
$173$	−22.1636			−1.68507			−0.842533	+	0.538645i	$0.818937\pi$
$174$	−2.27495	+	2.27495i	−0.172464	+	0.172464i
$175$	2.24330	−	6.82510i	0.169578	−	0.515929i
$176$	1.61073	+	6.01134i	0.121414	+	0.453122i
$177$	9.61514	+	2.57637i	0.722718	+	0.193652i
$178$	−2.48570	+	1.43512i	−0.186311	+	0.107567i
$179$		−	9.83448i		−	0.735064i	−0.930011	−	0.367532i	$-0.880203\pi$
$179$		−	9.83448i		−	0.735064i	0.930011	−	0.367532i	$-0.119797\pi$
$180$	1.45998	−	0.391201i	0.108821	−	0.0291584i
$181$	11.3170			0.841186			0.420593	−	0.907249i	$-0.361822\pi$
$181$	11.3170			0.841186			0.420593	+	0.907249i	$0.361822\pi$
$182$	−3.80996	+	8.74553i	−0.282413	+	0.648262i
$183$	0.829226			0.0612982
$184$	−0.0583833	+	0.0156437i	−0.00430407	+	0.00115327i
$185$		−	7.30127i		−	0.536800i
$186$	7.05576	−	4.07364i	0.517353	−	0.298694i
$187$	−45.1227	−	12.0906i	−3.29970	−	0.884151i
$188$	−0.335258	−	1.25120i	−0.0244512	−	0.0912531i
$189$	2.58979	−	0.541277i	0.188380	−	0.0393721i
$190$	−8.26176	+	8.26176i	−0.599371	+	0.599371i
$191$	−12.6308			−0.913932			−0.456966	−	0.889484i	$-0.651064\pi$
$191$	−12.6308			−0.913932			−0.456966	+	0.889484i	$0.651064\pi$
$192$	1.00000			0.0721688
$193$	−1.40376	+	1.40376i	−0.101045	+	0.101045i	−0.755822	−	0.654777i	$-0.772762\pi$
$193$	−1.40376	+	1.40376i	−0.101045	+	0.101045i	0.654777	+	0.755822i	$0.272762\pi$
$194$	−1.28215	−	2.22075i	−0.0920531	−	0.159441i
$195$	4.95293	−	2.27335i	0.354686	−	0.162798i
$196$	−4.15293	+	5.63500i	−0.296638	+	0.402500i
$197$	−0.930208	+	3.47158i	−0.0662746	+	0.247340i	−0.991113	−	0.133019i	$-0.957533\pi$
$197$	−0.930208	+	3.47158i	−0.0662746	+	0.247340i	0.924839	+	0.380359i	$0.124200\pi$
$198$	3.11170	−	5.38962i	0.221139	−	0.383023i
$199$	5.09416	+	8.82335i	0.361116	+	0.625471i	0.988145	−	0.153525i	$-0.0490626\pi$
$199$	5.09416	+	8.82335i	0.361116	+	0.625471i	−0.627029	+	0.778996i	$0.715729\pi$
$200$	−2.62289	+	0.702801i	−0.185466	+	0.0496955i
$201$	0.615467	−	0.615467i	0.0434117	−	0.0434117i
$202$	7.78173	−	2.08511i	0.547521	−	0.146708i
$203$	−6.34505	+	5.67415i	−0.445335	+	0.398247i
$204$	−3.75313	+	6.50061i	−0.262772	+	0.455134i
$205$	5.21479	+	3.01076i	0.364216	+	0.210280i
$206$	9.79642	+	9.79642i	0.682549	+	0.682549i
$207$	0.0523450	+	0.0302214i	0.00363823	+	0.00210053i
$208$	3.55448	−	0.604689i	0.246459	−	0.0419276i
$209$			48.1073i			3.32765i
$210$	3.91443	−	0.818131i	0.270121	−	0.0564564i
$211$	12.7116	+	22.0172i	0.875104	+	1.51573i	0.856652	+	0.515895i	$0.172541\pi$
$211$	12.7116	+	22.0172i	0.875104	+	1.51573i	0.0184528	+	0.999830i	$0.494126\pi$
$212$			3.63254i			0.249484i
$213$	−0.133304	−	0.497499i	−0.00913387	−	0.0340881i
$214$	2.68362	−	10.0154i	0.183448	−	0.684638i
$215$	−4.74767	−	4.74767i	−0.323788	−	0.323788i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	19.2394	−	9.72069i	1.30606	−	0.659884i
$218$	12.1859	−	7.03553i	0.825333	−	0.476506i
$219$	2.10970	+	7.87352i	0.142560	+	0.532043i
$220$	4.70328	−	8.14632i	0.317095	−	0.549225i
$221$	−9.40959	+	25.3758i	−0.632958	+	1.70696i
$222$	−4.18336	+	2.41526i	−0.280769	+	0.162102i
$223$	−10.2954	−	2.75865i	−0.689432	−	0.184733i	−0.102940	−	0.994688i	$-0.532825\pi$
$223$	−10.2954	−	2.75865i	−0.689432	−	0.184733i	−0.586492	+	0.809955i	$0.699492\pi$
$224$	2.64164	+	0.147454i	0.176502	+	0.00985221i
$225$	2.35162	+	1.35771i	0.156775	+	0.0905138i
$226$	−2.86049	+	10.6755i	−0.190277	+	0.710123i
$227$	2.56781	+	0.688042i	0.170431	+	0.0456670i	0.343026	−	0.939326i	$-0.388548\pi$
$227$	2.56781	+	0.688042i	0.170431	+	0.0456670i	−0.172594	+	0.984993i	$0.555215\pi$
$228$	7.46668	+	2.00069i	0.494493	+	0.132499i
$229$	0.650085	−	2.42615i	0.0429588	−	0.160324i	−0.941114	−	0.338088i	$-0.890220\pi$
$229$	0.650085	−	2.42615i	0.0429588	−	0.160324i	0.984073	+	0.177764i	$0.0568864\pi$
$230$	0.0791186	+	0.0456792i	0.00521693	+	0.00301200i
$231$	9.01470	−	13.7786i	0.593124	−	0.906565i
$232$	3.10764	+	0.832690i	0.204027	+	0.0546688i
$233$	17.7000	−	10.2191i	1.15957	−	0.669475i	0.208365	−	0.978051i	$-0.433186\pi$
$233$	17.7000	−	10.2191i	1.15957	−	0.669475i	0.951200	+	0.308576i	$0.0998523\pi$
$234$	−2.94098	−	2.08582i	−0.192258	−	0.136354i
$235$	−0.978941	+	1.69558i	−0.0638591	+	0.110607i
$236$	−2.57637	−	9.61514i	−0.167707	−	0.625892i
$237$	9.93222	−	5.73437i	0.645167	−	0.372487i
$238$	−10.8730	+	16.6189i	−0.704789	+	1.07724i
$239$	−12.0931	−	12.0931i	−0.782235	−	0.782235i	0.197972	−	0.980208i	$-0.436564\pi$
$239$	−12.0931	−	12.0931i	−0.782235	−	0.782235i	−0.980208	+	0.197972i	$0.936564\pi$
$240$	−1.06878	−	1.06878i	−0.0689895	−	0.0689895i
$241$	−1.73894	+	6.48980i	−0.112015	+	0.418045i	−0.999046	−	0.0436640i	$-0.986097\pi$
$241$	−1.73894	+	6.48980i	−0.112015	+	0.418045i	0.887031	+	0.461709i	$0.152764\pi$
$242$	−7.17721	−	26.7857i	−0.461369	−	1.72185i
$243$			1.00000i			0.0641500i
$244$	−0.414613	−	0.718131i	−0.0265429	−	0.0459736i
$245$	10.4611	−	1.58401i	0.668338	−	0.101199i
$246$		−	3.98384i		−	0.254001i
$247$	27.7500	+	2.59640i	1.76569	+	0.165205i
$248$	−7.05576	−	4.07364i	−0.448041	−	0.258677i
$249$	4.74859	+	4.74859i	0.300930	+	0.300930i
$250$	10.0994	+	5.83086i	0.638739	+	0.368776i
$251$	10.3549	−	17.9352i	0.653596	−	1.13206i	−0.328648	−	0.944453i	$-0.606593\pi$
$251$	10.3549	−	17.9352i	0.653596	−	1.13206i	0.982244	−	0.187609i	$-0.0600738\pi$
$252$	−1.76365	−	1.97219i	−0.111100	−	0.124236i
$253$	0.363342	−	0.0973572i	0.0228431	−	0.00612079i
$254$	−4.33060	+	4.33060i	−0.271726	+	0.271726i
$255$	10.9590	−	2.93646i	0.686280	−	0.183888i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.75383	+	8.23387i	−0.296536	+	0.513615i	−0.975341	−	0.220704i	$-0.929165\pi$
$257$	−4.75383	+	8.23387i	−0.296536	+	0.513615i	0.678805	+	0.734318i	$0.262498\pi$
$258$	−1.14971	+	4.29077i	−0.0715777	+	0.267132i
$259$	−11.4071	+	5.76340i	−0.708801	+	0.358120i
$260$	−4.44524	−	3.15268i	−0.275682	−	0.195521i
$261$	−1.60863	−	2.78623i	−0.0995719	−	0.172464i
$262$	8.16716	−	8.16716i	0.504569	−	0.504569i
$263$	17.8280			1.09932			0.549661	−	0.835388i	$-0.314757\pi$
$263$	17.8280			1.09932			0.549661	+	0.835388i	$0.314757\pi$
$264$	−6.22339			−0.383023
$265$	3.88239	−	3.88239i	0.238493	−	0.238493i
$266$	19.4293	+	6.38610i	1.19128	+	0.391557i
$267$	−0.742873	−	2.77244i	−0.0454631	−	0.169670i
$268$	−0.840744	−	0.225277i	−0.0513566	−	0.0137610i
$269$	−7.92939	+	4.57804i	−0.483464	+	0.279128i	−0.721859	−	0.692040i	$-0.756712\pi$
$269$	−7.92939	+	4.57804i	−0.483464	+	0.279128i	0.238395	+	0.971168i	$0.423379\pi$
$270$			1.51148i			0.0919860i
$271$	−16.4254	+	4.40116i	−0.997769	+	0.267351i	−0.720511	−	0.693444i	$-0.756093\pi$
$271$	−16.4254	+	4.40116i	−0.997769	+	0.267351i	−0.277258	+	0.960795i	$0.589426\pi$
$272$	7.50626			0.455134
$273$	−7.46144	−	5.94364i	−0.451587	−	0.359726i
$274$	4.24535			0.256471
$275$	16.3233	−	4.37381i	0.984330	−	0.263751i
$276$		−	0.0604428i		−	0.00363823i
$277$	−9.98812	+	5.76664i	−0.600128	+	0.346484i	−0.769092	−	0.639138i	$-0.779291\pi$
$277$	−9.98812	+	5.76664i	−0.600128	+	0.346484i	0.168964	+	0.985622i	$0.445958\pi$
$278$	8.41475	+	2.25472i	0.504683	+	0.135229i
$279$	2.10867	+	7.86967i	0.126243	+	0.471145i
$280$	−2.66574	−	2.98093i	−0.159308	−	0.178145i
$281$	10.6233	−	10.6233i	0.633736	−	0.633736i	−0.315267	−	0.949003i	$-0.602094\pi$
$281$	10.6233	−	10.6233i	0.633736	−	0.633736i	0.949003	+	0.315267i	$0.102094\pi$
$282$	1.29534			0.0771362
$283$	12.0916			0.718771			0.359386	−	0.933189i	$-0.382986\pi$
$283$	12.0916			0.718771			0.359386	+	0.933189i	$0.382986\pi$
$284$	−0.364195	+	0.364195i	−0.0216110	+	0.0216110i
$285$	−5.84194	−	10.1185i	−0.346047	−	0.599371i
$286$	−22.1209	+	3.76322i	−1.30804	+	0.222524i
$287$	0.587435	−	10.5239i	0.0346752	−	0.621205i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	−19.6720	+	34.0729i	−1.15718	+	2.00429i
$290$	−2.43142	−	4.21135i	−0.142778	−	0.247299i
$291$	2.47693	−	0.663690i	0.145200	−	0.0389062i
$292$	5.76381	−	5.76381i	0.337302	−	0.337302i
$293$	−7.51103	+	2.01257i	−0.438799	+	0.117576i	−0.471454	−	0.881891i	$-0.656271\pi$
$293$	−7.51103	+	2.01257i	−0.438799	+	0.117576i	0.0326547	+	0.999467i	$0.489604\pi$
$294$	−4.36813	−	5.46986i	−0.254755	−	0.319009i
$295$	−7.52290	+	13.0300i	−0.438000	+	0.758639i
$296$	4.18336	+	2.41526i	0.243153	+	0.140384i
$297$	4.40060	+	4.40060i	0.255349	+	0.255349i
$298$	−4.71289	−	2.72099i	−0.273010	−	0.157622i
$299$	−0.0365491	−	0.214843i	−0.00211369	−	0.0124247i
$300$		−	2.71542i		−	0.156775i
$301$	−3.66981	+	11.1651i	−0.211524	+	0.643548i
$302$	−6.85385	−	11.8712i	−0.394395	−	0.683111i
$303$			8.05624i			0.462819i
$304$	−2.00069	−	7.46668i	−0.114747	−	0.428243i
$305$	−0.324394	+	1.21065i	−0.0185747	+	0.0693219i
$306$	−5.30773	−	5.30773i	−0.303423	−	0.303423i
$307$	−0.870087	−	0.870087i	−0.0496585	−	0.0496585i	0.681841	−	0.731500i	$-0.261179\pi$
$307$	−0.870087	−	0.870087i	−0.0496585	−	0.0496585i	−0.731500	+	0.681841i	$0.761179\pi$
$308$	−16.4400	−	0.917667i	−0.936754	−	0.0522889i
$309$	−11.9981	+	6.92712i	−0.682549	+	0.394070i
$310$	3.18723	+	11.8949i	0.181022	+	0.675584i
$311$	−8.97807	+	15.5505i	−0.509100	+	0.881787i	0.490845	+	0.871247i	$0.336688\pi$
$311$	−8.97807	+	15.5505i	−0.509100	+	0.881787i	−0.999944	+	0.0105396i	$0.996645\pi$
$312$	−0.335884	+	3.58987i	−0.0190157	+	0.203236i
$313$	0.403027	−	0.232688i	0.0227804	−	0.0131523i	−0.488567	−	0.872527i	$-0.662480\pi$
$313$	0.403027	−	0.232688i	0.0227804	−	0.0131523i	0.511347	+	0.859374i	$0.329147\pi$
$314$	21.5586	+	5.77660i	1.21662	+	0.325992i
$315$	−0.222875	+	3.99280i	−0.0125576	+	0.224969i
$316$	−9.93222	−	5.73437i	−0.558731	−	0.322584i
$317$	−0.0422978	+	0.157858i	−0.00237568	+	0.00886617i	−0.967103	−	0.254383i	$-0.918128\pi$
$317$	−0.0422978	+	0.157858i	−0.00237568	+	0.00886617i	0.964728	+	0.263249i	$0.0847942\pi$
$318$	−3.50876	−	0.940170i	−0.196762	−	0.0527221i
$319$	−19.3401	−	5.18216i	−1.08284	−	0.290145i
$320$	−0.391201	+	1.45998i	−0.0218688	+	0.0816155i
$321$	8.97955	+	5.18435i	0.501190	+	0.289362i
$322$	0.00891256	−	0.159668i	0.000496677	−	0.00889795i
$323$	56.0468	+	15.0177i	3.11853	+	0.835607i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−1.64198	−	9.65190i	−0.0910807	−	0.535391i
$326$	−5.90355	+	10.2252i	−0.326967	+	0.566324i
$327$	3.64186	+	13.5916i	0.201395	+	0.751617i
$328$	−3.45011	+	1.99192i	−0.190500	+	0.109985i
$329$	3.42181	+	0.191003i	0.188651	+	0.0105303i
$330$	6.65144	+	6.65144i	0.366150	+	0.366150i
$331$	−8.31583	−	8.31583i	−0.457079	−	0.457079i	0.440616	−	0.897696i	$-0.354760\pi$
$331$	−8.31583	−	8.31583i	−0.457079	−	0.457079i	−0.897696	+	0.440616i	$0.854760\pi$
$332$	1.73811	−	6.48670i	0.0953909	−	0.356004i
$333$	−1.25023	−	4.66593i	−0.0685123	−	0.255691i
$334$		−	8.93020i		−	0.488639i
$335$	0.657800	+	1.13934i	0.0359394	+	0.0622489i
$336$	−0.826136	+	2.51346i	−0.0450694	+	0.137121i
$337$		−	18.5295i		−	1.00937i	−0.863304	−	0.504684i	$-0.831609\pi$
$337$		−	18.5295i		−	1.00937i	0.863304	−	0.504684i	$-0.168391\pi$
$338$	0.976863	+	12.9632i	0.0531343	+	0.705108i
$339$	−9.57138	−	5.52604i	−0.519846	−	0.300133i
$340$	−8.02255	−	8.02255i	−0.435084	−	0.435084i
$341$	43.9107	+	25.3519i	2.37790	+	1.37288i
$342$	−3.86504	+	6.69444i	−0.208997	+	0.361994i
$343$	−10.7325	−	15.0935i	−0.579499	−	0.814973i
$344$	4.29077	−	1.14971i	0.231343	−	0.0619881i
$345$	−0.0646001	+	0.0646001i	−0.00347795	+	0.00347795i
$346$	−21.4084	+	5.73636i	−1.15092	+	0.308389i
$347$	14.9443	+	25.8842i	0.802250	+	1.38954i	0.918132	+	0.396274i	$0.129697\pi$
$347$	14.9443	+	25.8842i	0.802250	+	1.38954i	−0.115883	+	0.993263i	$0.536970\pi$
$348$	−1.60863	+	2.78623i	−0.0862318	+	0.149358i
$349$	−2.72772	+	10.1800i	−0.146012	+	0.544923i	0.853697	+	0.520771i	$0.174355\pi$
$349$	−2.72772	+	10.1800i	−0.146012	+	0.544923i	−0.999708	+	0.0241523i	$0.992311\pi$
$350$	0.400400	−	7.17315i	0.0214023	−	0.383421i
$351$	2.77593	−	2.30092i	0.148168	−	0.122814i
$352$	3.11170	+	5.38962i	0.165854	+	0.287268i
$353$	25.1379	−	25.1379i	1.33796	−	1.33796i	0.439921	−	0.898037i	$-0.355007\pi$
$353$	25.1379	−	25.1379i	1.33796	−	1.33796i	0.898037	−	0.439921i	$-0.144993\pi$
$354$	9.95432			0.529066
$355$	0.778488			0.0413179
$356$	−2.02957	+	2.02957i	−0.107567	+	0.107567i
$357$	−13.2385	−	14.8038i	−0.700653	−	0.783498i
$358$	−2.54535	−	9.49938i	−0.134526	−	0.502058i
$359$	1.48348	+	0.397498i	0.0782952	+	0.0209791i	0.297754	−	0.954643i	$-0.403762\pi$
$359$	1.48348	+	0.397498i	0.0782952	+	0.0209791i	−0.219459	+	0.975622i	$0.570429\pi$
$360$	1.30898	−	0.755742i	0.0689895	−	0.0398311i
$361$		−	40.7540i		−	2.14495i
$362$	10.9314	−	2.92906i	0.574541	−	0.153948i
$363$	27.7306			1.45548
$364$	−1.41663	+	9.43362i	−0.0742513	+	0.494456i
$365$	−12.3205			−0.644885
$366$	0.800971	−	0.214619i	0.0418674	−	0.0112183i
$367$		−	5.51299i		−	0.287776i	−0.989594	−	0.143888i	$-0.954040\pi$
$367$		−	5.51299i		−	0.287776i	0.989594	−	0.143888i	$-0.0459605\pi$
$368$	−0.0523450	+	0.0302214i	−0.00272867	+	0.00157540i
$369$	3.84810	+	1.03109i	0.200324	+	0.0536766i
$370$	−1.88971	−	7.05248i	−0.0982412	−	0.366641i
$371$	−9.13025	−	3.00097i	−0.474019	−	0.155803i
$372$	5.76100	−	5.76100i	0.298694	−	0.298694i
$373$	−18.9455			−0.980959			−0.490480	−	0.871453i	$-0.663178\pi$
$373$	−18.9455			−0.980959			−0.490480	+	0.871453i	$0.663178\pi$
$374$	−46.7144			−2.41555
$375$	−8.24609	+	8.24609i	−0.425826	+	0.425826i
$376$	−0.647669	−	1.12180i	−0.0334010	−	0.0578522i
$377$	−4.03305	+	10.8763i	−0.207713	+	0.560160i
$378$	2.36145	−	1.19312i	0.121460	−	0.0613675i
$379$	−8.95565	+	33.4229i	−0.460021	+	1.71682i	0.212872	+	0.977080i	$0.431718\pi$
$379$	−8.95565	+	33.4229i	−0.460021	+	1.71682i	−0.672892	+	0.739740i	$0.734948\pi$
$380$	−5.84194	+	10.1185i	−0.299685	+	0.519070i
$381$	−3.06219	−	5.30387i	−0.156881	−	0.271726i
$382$	−12.2004	+	3.26909i	−0.624227	+	0.167261i
$383$	−16.4515	+	16.4515i	−0.840631	+	0.840631i	−0.988941	−	0.148310i	$-0.952617\pi$
$383$	−16.4515	+	16.4515i	−0.840631	+	0.840631i	0.148310	+	0.988941i	$0.452617\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	16.5899	+	18.5515i	0.845501	+	0.945472i
$386$	−0.992608	+	1.71925i	−0.0505224	+	0.0875073i
$387$	−3.84700	−	2.22107i	−0.195554	−	0.112903i
$388$	−1.81324	−	1.81324i	−0.0920531	−	0.0920531i
$389$	−17.4192	−	10.0570i	−0.883190	−	0.509910i	−0.0114814	−	0.999934i	$-0.503655\pi$
$389$	−17.4192	−	10.0570i	−0.883190	−	0.509910i	−0.871709	+	0.490024i	$0.836988\pi$
$390$	4.19577	−	3.47780i	0.212461	−	0.176105i
$391$		−	0.453699i		−	0.0229446i
$392$	−2.55298	+	6.51785i	−0.128945	+	0.329201i
$393$	5.77506	+	10.0027i	0.291313	+	0.504569i
$394$			3.59405i			0.181065i
$395$	4.48658	+	16.7442i	0.225745	+	0.842490i
$396$	1.61073	−	6.01134i	0.0809424	−	0.302081i
$397$	−10.7059	−	10.7059i	−0.537313	−	0.537313i	0.385426	−	0.922739i	$-0.374055\pi$
$397$	−10.7059	−	10.7059i	−0.537313	−	0.537313i	−0.922739	+	0.385426i	$0.874055\pi$
$398$	7.20424	+	7.20424i	0.361116	+	0.361116i
$399$	−11.1972	+	17.1144i	−0.560559	+	0.856791i
$400$	−2.35162	+	1.35771i	−0.117581	+	0.0678854i
$401$	−4.90270	−	18.2971i	−0.244829	−	0.913716i	−0.973469	−	0.228818i	$-0.926514\pi$
$401$	−4.90270	−	18.2971i	−0.244829	−	0.913716i	0.728640	−	0.684897i	$-0.240153\pi$
$402$	0.435201	−	0.753791i	0.0217059	−	0.0375957i
$403$	16.9938	−	23.9610i	0.846520	−	1.19358i
$404$	6.97691	−	4.02812i	0.347114	−	0.200407i
$405$	−1.45998	−	0.391201i	−0.0725471	−	0.0194389i
$406$	−4.66027	+	7.12303i	−0.231285	+	0.353510i
$407$	−26.0347	−	15.0311i	−1.29049	−	0.745066i
$408$	−1.94276	+	7.25049i	−0.0961811	+	0.358953i
$409$	26.2713	+	7.03936i	1.29903	+	0.348074i	0.841083	−	0.540906i	$-0.181918\pi$
$409$	26.2713	+	7.03936i	1.29903	+	0.348074i	0.457947	+	0.888980i	$0.348585\pi$
$410$	5.81634	+	1.55848i	0.287248	+	0.0769680i
$411$	−1.09878	+	4.10069i	−0.0541987	+	0.202272i
$412$	11.9981	+	6.92712i	0.591105	+	0.341275i
$413$	26.2957	+	1.46781i	1.29393	+	0.0722261i
$414$	0.0583833	+	0.0156437i	0.00286938	+	0.000768848i
$415$	−8.79051	+	5.07521i	−0.431509	+	0.249132i
$416$	3.27686	−	1.50405i	0.160661	−	0.0737422i
$417$	−4.35579	+	7.54445i	−0.213304	+	0.369454i
$418$	12.4511	+	46.4681i	0.609002	+	2.27283i
$419$	−6.33740	+	3.65890i	−0.309602	+	0.178749i	−0.646748	−	0.762703i	$-0.723872\pi$
$419$	−6.33740	+	3.65890i	−0.309602	+	0.178749i	0.337146	+	0.941452i	$0.390538\pi$
$420$	3.56930	−	1.80338i	0.174164	−	0.0879961i
$421$	−14.2023	−	14.2023i	−0.692178	−	0.692178i	0.270532	−	0.962711i	$-0.412800\pi$
$421$	−14.2023	−	14.2023i	−0.692178	−	0.692178i	−0.962711	+	0.270532i	$0.912800\pi$
$422$	17.9770	+	17.9770i	0.875104	+	0.875104i
$423$	−0.335258	+	1.25120i	−0.0163008	+	0.0608354i
$424$	0.940170	+	3.50876i	0.0456587	+	0.170401i
$425$		−	20.3826i		−	0.988702i
$426$	−0.257524	−	0.446045i	−0.0124771	−	0.0216110i
$427$	2.14752	−	0.448841i	0.103926	−	0.0217209i
$428$		−	10.3687i		−	0.501190i
$429$	2.09034	−	22.3412i	0.100922	−	1.07864i
$430$	−5.81468	−	3.35711i	−0.280409	−	0.161894i
$431$	2.22484	+	2.22484i	0.107167	+	0.107167i	0.758657	−	0.651490i	$-0.225856\pi$
$431$	2.22484	+	2.22484i	0.107167	+	0.107167i	−0.651490	+	0.758657i	$0.725856\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−0.586750	+	1.01628i	−0.0281974	+	0.0488394i	−0.879780	−	0.475381i	$-0.842310\pi$
$433$	−0.586750	+	1.01628i	−0.0281974	+	0.0488394i	0.851582	+	0.524221i	$0.175643\pi$
$434$	16.0680	−	14.3690i	0.771287	−	0.689734i
$435$	4.69715	−	1.25860i	0.225211	−	0.0603451i
$436$	9.94974	−	9.94974i	0.476506	−	0.476506i
$437$	−0.451307	+	0.120927i	−0.0215889	+	0.00578474i
$438$	4.07563	+	7.05920i	0.194741	+	0.337302i
$439$	−14.0026	+	24.2533i	−0.668310	+	1.15755i	0.310067	+	0.950715i	$0.399649\pi$
$439$	−14.0026	+	24.2533i	−0.668310	+	1.15755i	−0.978376	+	0.206832i	$0.933685\pi$
$440$	2.43460	−	9.08604i	0.116065	−	0.433160i
$441$	6.41404	−	2.80359i	0.305430	−	0.133504i
$442$	−2.52123	+	26.9465i	−0.119923	+	1.28172i
$443$	−7.27687	−	12.6039i	−0.345734	−	0.598830i	0.639752	−	0.768581i	$-0.279037\pi$
$443$	−7.27687	−	12.6039i	−0.345734	−	0.598830i	−0.985487	+	0.169751i	$0.945704\pi$
$444$	−3.41570	+	3.41570i	−0.162102	+	0.162102i
$445$	4.33832			0.205656
$446$	−10.6586			−0.504699
$447$	3.84805	−	3.84805i	0.182007	−	0.182007i
$448$	2.58979	−	0.541277i	0.122356	−	0.0255729i
$449$	8.54677	+	31.8970i	0.403347	+	1.50531i	0.807084	+	0.590437i	$0.201044\pi$
$449$	8.54677	+	31.8970i	0.403347	+	1.50531i	−0.403737	+	0.914875i	$0.632289\pi$
$450$	2.62289	+	0.702801i	0.123644	+	0.0331304i
$451$	21.4714	−	12.3965i	1.01105	−	0.583729i
$452$			11.0521i			0.519846i
$453$	13.2406	−	3.54781i	0.622098	−	0.166691i
$454$	2.65839			0.124765
$455$	11.5965	−	8.56841i	0.543654	−	0.401693i
$456$	7.73007			0.361994
$457$	−22.6788	+	6.07676i	−1.06087	+	0.284259i	−0.746736	−	0.665120i	$-0.768380\pi$
$457$	−22.6788	+	6.07676i	−1.06087	+	0.284259i	−0.314132	+	0.949379i	$0.601714\pi$
$458$		−	2.51173i		−	0.117366i
$459$	6.50061	−	3.75313i	0.303423	−	0.175181i
$460$	0.0882454	+	0.0236453i	0.00411446	+	0.00110247i
$461$	−7.65826	−	28.5810i	−0.356681	−	1.33115i	−0.878356	−	0.478007i	$-0.841359\pi$
$461$	−7.65826	−	28.5810i	−0.356681	−	1.33115i	0.521675	−	0.853144i	$-0.325307\pi$
$462$	5.14137	−	15.6423i	0.239198	−	0.727744i
$463$	−15.1405	+	15.1405i	−0.703641	+	0.703641i	−0.965190	−	0.261549i	$-0.915767\pi$
$463$	−15.1405	+	15.1405i	−0.703641	+	0.703641i	0.261549	+	0.965190i	$0.415767\pi$
$464$	3.21727			0.149358
$465$	−12.3145			−0.571071
$466$	14.4520	−	14.4520i	0.669475	−	0.669475i
$467$	−14.4895	−	25.0965i	−0.670493	−	1.16133i	−0.977765	−	0.209706i	$-0.932749\pi$
$467$	−14.4895	−	25.0965i	−0.670493	−	1.16133i	0.307272	−	0.951622i	$-0.400584\pi$
$468$	−3.38062	−	1.25357i	−0.156269	−	0.0579461i
$469$	1.26079	−	1.92707i	0.0582181	−	0.0889838i
$470$	−0.506737	+	1.89117i	−0.0233740	+	0.0872331i
$471$	−11.1595	+	19.3289i	−0.514204	+	0.890628i
$472$	−4.97716	−	8.62070i	−0.229092	−	0.396800i
$473$	−26.7032	+	7.15509i	−1.22781	+	0.328991i
$474$	8.10963	−	8.10963i	0.372487	−	0.372487i
$475$	−20.2751	+	5.43270i	−0.930287	+	0.249270i
$476$	−6.20120	+	18.8667i	−0.284231	+	0.864754i
$477$	1.81627	−	3.14587i	0.0831613	−	0.144040i
$478$	−14.8109	−	8.55109i	−0.677435	−	0.391118i
$479$	−20.7600	−	20.7600i	−0.948550	−	0.948550i	0.0501896	−	0.998740i	$-0.484017\pi$
$479$	−20.7600	−	20.7600i	−0.948550	−	0.948550i	−0.998740	+	0.0501896i	$0.984017\pi$
$480$	−1.30898	−	0.755742i	−0.0597467	−	0.0344948i
$481$	−10.0756	+	14.2065i	−0.459408	+	0.647760i
$482$			6.71874i			0.306030i
$483$	0.151921	+	0.0499340i	0.00691263	+	0.00227208i
$484$	−13.8653	−	24.0154i	−0.630242	−	1.09161i
$485$			3.87590i			0.175996i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	7.43946	−	27.7645i	0.337114	−	1.25813i	−0.564445	−	0.825471i	$-0.690910\pi$
$487$	7.43946	−	27.7645i	0.337114	−	1.25813i	0.901559	−	0.432657i	$-0.142424\pi$
$488$	−0.586351	−	0.586351i	−0.0265429	−	0.0265429i
$489$	−8.34888	−	8.34888i	−0.377549	−	0.377549i
$490$	9.69472	−	4.23758i	0.437963	−	0.191434i
$491$	27.7851	−	16.0417i	1.25392	−	0.723953i	0.282038	−	0.959403i	$-0.408990\pi$
$491$	27.7851	−	16.0417i	1.25392	−	0.723953i	0.971887	+	0.235450i	$0.0756563\pi$
$492$	−1.03109	−	3.84810i	−0.0464853	−	0.173486i
$493$	−12.0748	+	20.9142i	−0.543823	+	0.941928i
$494$	27.4764	−	4.67429i	1.23622	−	0.210306i
$495$	−8.14632	+	4.70328i	−0.366150	+	0.211397i
$496$	−7.86967	−	2.10867i	−0.353359	−	0.0946822i
$497$	−0.614515	−	1.21626i	−0.0275648	−	0.0545569i
$498$	5.81582	+	3.35776i	0.260613	+	0.150465i
$499$	0.861922	−	3.21674i	0.0385849	−	0.144001i	−0.943946	−	0.330099i	$-0.892918\pi$
$499$	0.861922	−	3.21674i	0.0385849	−	0.144001i	0.982531	+	0.186099i	$0.0595844\pi$
$500$	11.2644	+	3.01828i	0.503758	+	0.134981i
$501$	8.62592	+	2.31131i	0.385377	+	0.103262i
$502$	5.36010	−	20.0042i	0.239233	−	0.892829i
$503$	−35.7390	−	20.6339i	−1.59352	−	0.920020i	−0.992696	−	0.120640i	$-0.961505\pi$
$503$	−35.7390	−	20.6339i	−1.59352	−	0.920020i	−0.600825	−	0.799380i	$-0.705161\pi$
$504$	−2.21400	−	1.44852i	−0.0986194	−	0.0645222i
$505$	−11.7620	−	3.15161i	−0.523401	−	0.140245i
$506$	0.325764	−	0.188080i	0.0144820	−	0.00836116i
$507$	−12.7744	−	2.41156i	−0.567329	−	0.107101i
$508$	−3.06219	+	5.30387i	−0.135863	+	0.235321i
$509$	6.68840	+	24.9615i	0.296458	+	1.10640i	0.940052	+	0.341030i	$0.110776\pi$
$509$	6.68840	+	24.9615i	0.296458	+	1.10640i	−0.643594	+	0.765367i	$0.722557\pi$
$510$	9.82558	−	5.67280i	0.435084	−	0.251196i
$511$	9.72544	+	19.2488i	0.430228	+	0.851518i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−5.46599	−	5.46599i	−0.241329	−	0.241329i
$514$	−2.46076	+	9.18369i	−0.108540	+	0.405075i
$515$	−5.41979	−	20.2269i	−0.238824	−	0.891305i
$516$			4.44213i			0.195554i
$517$	4.03070	+	6.98137i	0.177270	+	0.307040i
$518$	−9.52670	+	8.51938i	−0.418579	+	0.374320i
$519$		−	22.1636i		−	0.972873i
$520$	−5.10975	−	1.89475i	−0.224077	−	0.0830901i
$521$	−8.66539	−	5.00297i	−0.379638	−	0.219184i	0.298023	−	0.954559i	$-0.403673\pi$
$521$	−8.66539	−	5.00297i	−0.379638	−	0.219184i	−0.677661	+	0.735375i	$0.737006\pi$
$522$	−2.27495	−	2.27495i	−0.0995719	−	0.0995719i
$523$	−34.5919	−	19.9716i	−1.51260	−	0.873299i	−0.999891	−	0.0147357i	$-0.995309\pi$
$523$	−34.5919	−	19.9716i	−1.51260	−	0.873299i	−0.512707	−	0.858564i	$-0.671357\pi$
$524$	5.77506	−	10.0027i	0.252284	−	0.436970i
$525$	6.82510	+	2.24330i	0.297872	+	0.0979058i
$526$	17.2205	−	4.61423i	0.750851	−	0.201190i
$527$	43.2436	−	43.2436i	1.88372	−	1.88372i
$528$	−6.01134	+	1.61073i	−0.261610	+	0.0700981i
$529$	−11.4982	−	19.9154i	−0.499921	−	0.865888i
$530$	2.74526	−	4.75493i	0.119247	−	0.206541i
$531$	−2.57637	+	9.61514i	−0.111805	+	0.417261i
$532$	20.4201	+	1.13983i	0.885322	+	0.0494180i
$533$	−5.99191	−	13.0545i	−0.259538	−	0.565453i
$534$	−1.43512	−	2.48570i	−0.0621037	−	0.107567i
$535$	−11.0819	+	11.0819i	−0.479111	+	0.479111i
$536$	−0.870402			−0.0375957
$537$	9.83448			0.424389
$538$	−6.47432	+	6.47432i	−0.279128	+	0.279128i
$539$	15.8882	−	40.5631i	0.684352	−	1.74718i
$540$	0.391201	+	1.45998i	0.0168346	+	0.0628276i
$541$	−21.8557	−	5.85623i	−0.939652	−	0.251779i	−0.243686	−	0.969854i	$-0.578357\pi$
$541$	−21.8557	−	5.85623i	−0.939652	−	0.251779i	−0.695966	+	0.718075i	$0.745023\pi$
$542$	−14.7266	+	8.50239i	−0.632560	+	0.365209i
$543$			11.3170i			0.485659i
$544$	7.25049	−	1.94276i	0.310862	−	0.0832953i
$545$	−21.2682			−0.911029
$546$	−8.74553	−	3.80996i	−0.374274	−	0.163051i
$547$	35.2646			1.50781			0.753904	−	0.656985i	$-0.228168\pi$
$547$	35.2646			1.50781			0.753904	+	0.656985i	$0.228168\pi$
$548$	4.10069	−	1.09878i	0.175173	−	0.0469374i
$549$			0.829226i			0.0353905i
$550$	14.6350	−	8.44955i	0.624041	−	0.360290i
$551$	24.0223	+	6.43675i	1.02338	+	0.274215i
$552$	−0.0156437	−	0.0583833i	−0.000665842	−	0.00248496i
$553$	22.6185	−	20.2269i	0.961837	−	0.860136i
$554$	−8.15527	+	8.15527i	−0.346484	+	0.346484i
$555$	7.30127			0.309922
$556$	8.71159			0.369454
$557$	7.82849	−	7.82849i	0.331704	−	0.331704i	−0.521530	−	0.853233i	$-0.674638\pi$
$557$	7.82849	−	7.82849i	0.331704	−	0.331704i	0.853233	+	0.521530i	$0.174638\pi$
$558$	4.07364	+	7.05576i	0.172451	+	0.298694i
$559$	2.68611	+	15.7895i	0.113610	+	0.667824i
$560$	−3.34643	−	2.18941i	−0.141412	−	0.0925196i
$561$	12.0906	−	45.1227i	0.510465	−	1.90508i
$562$	7.51184	−	13.0109i	0.316868	−	0.548831i
$563$	−7.90232	−	13.6872i	−0.333043	−	0.576848i	0.650064	−	0.759880i	$-0.274742\pi$
$563$	−7.90232	−	13.6872i	−0.333043	−	0.576848i	−0.983107	+	0.183032i	$0.941409\pi$
$564$	1.25120	−	0.335258i	0.0526850	−	0.0141169i
$565$	11.8122	−	11.8122i	0.496945	−	0.496945i
$566$	11.6796	−	3.12954i	0.490930	−	0.131544i
$567$	0.541277	+	2.58979i	0.0227315	+	0.108761i
$568$	−0.257524	+	0.446045i	−0.0108055	+	0.0187157i
$569$	34.2970	+	19.8014i	1.43781	+	0.830118i	0.997697	−	0.0678257i	$-0.0216062\pi$
$569$	34.2970	+	19.8014i	1.43781	+	0.830118i	0.440110	+	0.897944i	$0.354940\pi$
$570$	−8.26176	−	8.26176i	−0.346047	−	0.346047i
$571$	9.31305	+	5.37689i	0.389739	+	0.225016i	0.682047	−	0.731308i	$-0.261090\pi$
$571$	9.31305	+	5.37689i	0.389739	+	0.225016i	−0.292308	+	0.956324i	$0.594423\pi$
$572$	−20.3932	+	9.36031i	−0.852683	+	0.391374i
$573$		−	12.6308i		−	0.527659i
$574$	−2.15636	−	10.3173i	−0.0900047	−	0.430637i
$575$	0.0820636	+	0.142138i	0.00342229	+	0.00592758i
$576$			1.00000i			0.0416667i
$577$	−5.14672	−	19.2078i	−0.214261	−	0.799633i	−0.986425	−	0.164210i	$-0.947493\pi$
$577$	−5.14672	−	19.2078i	−0.214261	−	0.799633i	0.772165	−	0.635423i	$-0.219174\pi$
$578$	−10.1830	+	38.0033i	−0.423556	+	1.58073i
$579$	−1.40376	−	1.40376i	−0.0583382	−	0.0583382i
$580$	−3.43855	−	3.43855i	−0.142778	−	0.142778i
$581$	14.8682	+	9.72756i	0.616836	+	0.403567i
$582$	2.22075	−	1.28215i	0.0920531	−	0.0531469i
$583$	−5.85105	−	21.8364i	−0.242326	−	0.904372i
$584$	4.07563	−	7.05920i	0.168651	−	0.292112i
$585$	2.27335	+	4.95293i	0.0939915	+	0.204778i
$586$	−6.73420	+	3.88799i	−0.278187	+	0.160612i
$587$	14.9755	+	4.01267i	0.618104	+	0.165621i	0.554266	−	0.832340i	$-0.312999\pi$
$587$	14.9755	+	4.01267i	0.618104	+	0.165621i	0.0638384	+	0.997960i	$0.479666\pi$
$588$	−5.63500	−	4.15293i	−0.232383	−	0.171264i
$589$	−54.5415	−	31.4896i	−2.24734	−	1.29750i
$590$	−3.89414	+	14.5331i	−0.160319	+	0.598319i
$591$	−3.47158	−	0.930208i	−0.142802	−	0.0382636i
$592$	4.66593	+	1.25023i	0.191769	+	0.0513842i
$593$	11.2653	−	42.0426i	0.462609	−	1.72648i	−0.202086	−	0.979368i	$-0.564772\pi$
$593$	11.2653	−	42.0426i	0.462609	−	1.72648i	0.664696	−	0.747114i	$-0.268561\pi$
$594$	5.38962	+	3.11170i	0.221139	+	0.127674i
$595$	26.7921	−	13.5367i	1.09837	−	0.554949i
$596$	−5.25654	−	1.40849i	−0.215316	−	0.0576938i
$597$	−8.82335	+	5.09416i	−0.361116	+	0.208490i
$598$	−0.0909091	−	0.198063i	−0.00371755	−	0.00809939i
$599$	−5.85128	+	10.1347i	−0.239077	+	0.414093i	−0.960450	−	0.278454i	$-0.910178\pi$
$599$	−5.85128	+	10.1347i	−0.239077	+	0.414093i	0.721373	+	0.692547i	$0.243511\pi$
$600$	−0.702801	−	2.62289i	−0.0286917	−	0.107079i
$601$	13.8487	−	7.99556i	0.564901	−	0.326146i	−0.190209	−	0.981744i	$-0.560917\pi$
$601$	13.8487	−	7.99556i	0.564901	−	0.326146i	0.755110	+	0.655598i	$0.227583\pi$
$602$	−0.655012	+	11.7345i	−0.0266963	+	0.478263i
$603$	0.615467	+	0.615467i	0.0250638	+	0.0250638i
$604$	−9.69280	−	9.69280i	−0.394395	−	0.394395i
$605$	−10.8482	+	40.4862i	−0.441044	+	1.64600i
$606$	2.08511	+	7.78173i	0.0847018	+	0.316111i
$607$			6.38329i			0.259090i	0.991574	+	0.129545i	$0.0413516\pi$
$607$			6.38329i			0.259090i	−0.991574	+	0.129545i	$0.958648\pi$
$608$	−3.86504	−	6.69444i	−0.156748	−	0.271495i
$609$	−5.67415	−	6.34505i	−0.229928	−	0.257114i
$610$			1.25336i			0.0507472i
$611$	4.24464	−	1.94826i	0.171720	−	0.0788180i
$612$	−6.50061	−	3.75313i	−0.262772	−	0.151711i
$613$	33.2418	+	33.2418i	1.34262	+	1.34262i	0.893441	+	0.449181i	$0.148284\pi$
$613$	33.2418	+	33.2418i	1.34262	+	1.34262i	0.449181	+	0.893441i	$0.351716\pi$
$614$	−1.06564	−	0.615245i	−0.0430055	−	0.0248293i
$615$	−3.01076	+	5.21479i	−0.121405	+	0.210280i
$616$	−16.1173	+	3.36858i	−0.649384	+	0.135724i
$617$	−16.0799	+	4.30860i	−0.647354	+	0.173458i	−0.567532	−	0.823351i	$-0.692102\pi$
$617$	−16.0799	+	4.30860i	−0.647354	+	0.173458i	−0.0798215	+	0.996809i	$0.525435\pi$
$618$	−9.79642	+	9.79642i	−0.394070	+	0.394070i
$619$	27.3998	−	7.34176i	1.10129	−	0.295090i	0.338001	−	0.941146i	$-0.390249\pi$
$619$	27.3998	−	7.34176i	1.10129	−	0.295090i	0.763290	+	0.646055i	$0.223583\pi$
$620$	6.15725	+	10.6647i	0.247281	+	0.428303i
$621$	−0.0302214	+	0.0523450i	−0.00121274	+	0.00210053i
$622$	−4.64739	+	17.3443i	−0.186343	+	0.695443i
$623$	−3.42454	−	6.77794i	−0.137201	−	0.271552i
$624$	0.604689	+	3.55448i	0.0242069	+	0.142293i
$625$	−2.02472	−	3.50692i	−0.0809889	−	0.140277i
$626$	0.329070	−	0.329070i	0.0131523	−	0.0131523i
$627$	−48.1073			−1.92122
$628$	22.3191			0.890628
$629$	−25.6391	+	25.6391i	−1.02230	+	1.02230i
$630$	0.818131	+	3.91443i	0.0325951	+	0.155955i
$631$	−6.29363	−	23.4882i	−0.250546	−	0.935049i	−0.970515	−	0.241043i	$-0.922511\pi$
$631$	−6.29363	−	23.4882i	−0.250546	−	0.935049i	0.719969	−	0.694006i	$-0.244156\pi$
$632$	−11.0780	−	2.96833i	−0.440657	−	0.118074i
$633$	−22.0172	+	12.7116i	−0.875104	+	0.505242i
$634$			0.163426i			0.00649049i
$635$	8.94149	−	2.39587i	0.354832	−	0.0950770i
$636$	−3.63254			−0.144040
$637$	−22.5407	−	11.3541i	−0.893096	−	0.449866i
$638$	−20.0223			−0.792691
$639$	0.497499	−	0.133304i	0.0196808	−	0.00527344i
$640$			1.51148i			0.0597467i
$641$	24.0979	−	13.9129i	0.951808	−	0.549527i	0.0581661	−	0.998307i	$-0.481475\pi$
$641$	24.0979	−	13.9129i	0.951808	−	0.549527i	0.893642	+	0.448780i	$0.148141\pi$
$642$	10.0154	+	2.68362i	0.395276	+	0.105914i
$643$	−5.95094	−	22.2092i	−0.234682	−	0.875846i	−0.978292	−	0.207232i	$-0.933555\pi$
$643$	−5.95094	−	22.2092i	−0.234682	−	0.875846i	0.743610	−	0.668614i	$-0.233112\pi$
$644$	−0.0327163	−	0.156534i	−0.00128920	−	0.00616831i
$645$	4.74767	−	4.74767i	0.186939	−	0.186939i
$646$	58.0240			2.28292
$647$	11.5639			0.454623			0.227312	−	0.973822i	$-0.427006\pi$
$647$	11.5639			0.454623			0.227312	+	0.973822i	$0.427006\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	30.9748	+	53.6500i	1.21587	+	2.10595i
$650$	−4.08413	−	8.89804i	−0.160193	−	0.349010i
$651$	9.72069	+	19.2394i	0.380984	+	0.754053i
$652$	−3.05590	+	11.4048i	−0.119678	+	0.446646i
$653$	−4.11787	+	7.13236i	−0.161145	+	0.279111i	−0.935279	−	0.353910i	$-0.884852\pi$
$653$	−4.11787	+	7.13236i	−0.161145	+	0.279111i	0.774135	+	0.633021i	$0.218185\pi$
$654$	7.03553	+	12.1859i	0.275111	+	0.476506i
$655$	−16.8630	+	4.51841i	−0.658890	+	0.176549i
$656$	−2.81700	+	2.81700i	−0.109985	+	0.109985i
$657$	−7.87352	+	2.10970i	−0.307175	+	0.0823073i
$658$	3.35465	−	0.701136i	0.130778	−	0.0273331i
$659$	−12.9134	+	22.3667i	−0.503036	+	0.871283i	0.496958	+	0.867774i	$0.334450\pi$
$659$	−12.9134	+	22.3667i	−0.503036	+	0.871283i	−0.999994	+	0.00350872i	$0.998883\pi$
$660$	8.14632	+	4.70328i	0.317095	+	0.183075i
$661$	−19.3713	−	19.3713i	−0.753456	−	0.753456i	0.221666	−	0.975123i	$-0.428850\pi$
$661$	−19.3713	−	19.3713i	−0.753456	−	0.753456i	−0.975123	+	0.221666i	$0.928850\pi$
$662$	−10.1848	−	5.88018i	−0.395842	−	0.228540i
$663$	−25.3758	−	9.40959i	−0.985514	−	0.365438i
$664$		−	6.71552i		−	0.260613i
$665$	−20.6063	−	23.0428i	−0.799080	−	0.893562i
$666$	−2.41526	−	4.18336i	−0.0935896	−	0.162102i
$667$		−	0.194461i		−	0.00752954i
$668$	−2.31131	−	8.62592i	−0.0894272	−	0.333747i
$669$	2.75865	−	10.2954i	0.106655	−	0.398044i
$670$	0.930269	+	0.930269i	0.0359394	+	0.0359394i
$671$	3.64910	+	3.64910i	0.140872	+	0.140872i
$672$	−0.147454	+	2.64164i	−0.00568818	+	0.101903i
$673$	−19.5143	+	11.2666i	−0.752220	+	0.434294i	−0.826495	−	0.562943i	$-0.809669\pi$
$673$	−19.5143	+	11.2666i	−0.752220	+	0.434294i	0.0742756	+	0.997238i	$0.476336\pi$
$674$	−4.79580	−	17.8982i	−0.184727	−	0.689411i
$675$	−1.35771	+	2.35162i	−0.0522582	+	0.0905138i
$676$	4.29871	+	12.2687i	0.165335	+	0.471873i
$677$	−3.48362	+	2.01127i	−0.133886	+	0.0772994i	−0.565447	−	0.824785i	$-0.691296\pi$
$677$	−3.48362	+	2.01127i	−0.133886	+	0.0772994i	0.431561	+	0.902084i	$0.357963\pi$
$678$	−10.6755	−	2.86049i	−0.409990	−	0.109856i
$679$	6.05548	−	3.05952i	0.232388	−	0.117414i
$680$	−9.82558	−	5.67280i	−0.376794	−	0.217542i
$681$	−0.688042	+	2.56781i	−0.0263658	+	0.0983987i
$682$	48.9761	+	13.1231i	1.87539	+	0.502509i
$683$	−3.15425	−	0.845179i	−0.120694	−	0.0323399i	0.197966	−	0.980209i	$-0.436566\pi$
$683$	−3.15425	−	0.845179i	−0.120694	−	0.0323399i	−0.318660	+	0.947869i	$0.603233\pi$
$684$	−2.00069	+	7.46668i	−0.0764983	+	0.285496i
$685$	−5.55709	−	3.20839i	−0.212326	−	0.122586i
$686$	−14.2733	−	11.8014i	−0.544956	−	0.450581i
$687$	2.42615	+	0.650085i	0.0925633	+	0.0248023i
$688$	3.84700	−	2.22107i	0.146666	−	0.0846774i
$689$	−12.9118	+	2.19656i	−0.491900	+	0.0836821i
$690$	−0.0456792	+	0.0791186i	−0.00173898	+	0.00301200i
$691$	4.35797	+	16.2642i	0.165785	+	0.618718i	0.997939	+	0.0641730i	$0.0204410\pi$
$691$	4.35797	+	16.2642i	0.165785	+	0.618718i	−0.832154	+	0.554545i	$0.812892\pi$
$692$	−19.1942	+	11.0818i	−0.729655	+	0.421267i
$693$	13.7786	+	9.01470i	0.523405	+	0.342440i
$694$	21.1344	+	21.1344i	0.802250	+	0.802250i
$695$	−9.31078	−	9.31078i	−0.353178	−	0.353178i
$696$	−0.832690	+	3.10764i	−0.0315630	+	0.117795i
$697$	−7.73966	−	28.8848i	−0.293161	−	1.09409i
$698$			10.5391i			0.398911i
$699$	10.2191	+	17.7000i	0.386522	+	0.669475i
$700$	−1.46979	−	7.03236i	−0.0555529	−	0.265798i
$701$			7.65213i			0.289017i	0.989504	+	0.144509i	$0.0461601\pi$
$701$			7.65213i			0.289017i	−0.989504	+	0.144509i	$0.953840\pi$
$702$	2.08582	−	2.94098i	0.0787242	−	0.111000i
$703$	32.3377	+	18.6702i	1.21964	+	0.704159i
$704$	4.40060	+	4.40060i	0.165854	+	0.165854i
$705$	−1.69558	−	0.978941i	−0.0638591	−	0.0368691i
$706$	17.7752	−	30.7876i	0.668979	−	1.15871i
$707$	4.36066	+	20.8640i	0.163999	+	0.784671i
$708$	9.61514	−	2.57637i	0.361359	−	0.0968258i
$709$	3.57691	−	3.57691i	0.134334	−	0.134334i	−0.636743	−	0.771076i	$-0.719719\pi$
$709$	3.57691	−	3.57691i	0.134334	−	0.134334i	0.771076	+	0.636743i	$0.219719\pi$
$710$	0.751962	−	0.201488i	0.0282206	−	0.00756170i
$711$	5.73437	+	9.93222i	0.215056	+	0.372487i
$712$	−1.43512	+	2.48570i	−0.0537834	+	0.0931556i
$713$	−0.127454	+	0.475665i	−0.00477319	+	0.0178138i
$714$	−16.6189	−	10.8730i	−0.621945	−	0.406910i
$715$	31.8000	+	11.7917i	1.18925	+	0.440986i
$716$	−4.91724	−	8.51691i	−0.183766	−	0.318292i
$717$	12.0931	−	12.0931i	0.451624	−	0.451624i
$718$	1.53581			0.0573161
$719$	28.5362			1.06422			0.532110	−	0.846675i	$-0.321399\pi$
$719$	28.5362			1.06422			0.532110	+	0.846675i	$0.321399\pi$
$720$	1.06878	−	1.06878i	0.0398311	−	0.0398311i
$721$	−27.3231	+	24.4341i	−1.01757	+	0.909973i
$722$	−10.5479	−	39.3654i	−0.392553	−	1.46503i
$723$	−6.48980	−	1.73894i	−0.241358	−	0.0646718i
$724$	9.80082	−	5.65850i	0.364244	−	0.210297i
$725$		−	8.73621i		−	0.324455i
$726$	26.7857	−	7.17721i	0.994112	−	0.266371i
$727$	−23.9463			−0.888119			−0.444060	−	0.895997i	$-0.646462\pi$
$727$	−23.9463			−0.888119			−0.444060	+	0.895997i	$0.646462\pi$
$728$	1.07325	+	9.47883i	0.0397771	+	0.351309i
$729$	−1.00000			−0.0370370
$730$	−11.9007	+	3.18878i	−0.440465	+	0.118022i
$731$			33.3438i			1.23327i
$732$	0.718131	−	0.414613i	0.0265429	−	0.0153245i
$733$	44.8705	+	12.0230i	1.65733	+	0.444080i	0.961652	−	0.274274i	$-0.0884374\pi$
$733$	44.8705	+	12.0230i	1.65733	+	0.444080i	0.695678	+	0.718354i	$0.255104\pi$
$734$	−1.42687	−	5.32514i	−0.0526666	−	0.196554i
$735$	1.58401	+	10.4611i	0.0584270	+	0.385865i
$736$	−0.0427395	+	0.0427395i	−0.00157540	+	0.00157540i
$737$	5.41686			0.199532
$738$	3.98384			0.146647
$739$	−13.2967	+	13.2967i	−0.489128	+	0.489128i	−0.908031	−	0.418903i	$-0.862415\pi$
$739$	−13.2967	+	13.2967i	−0.489128	+	0.489128i	0.418903	+	0.908031i	$0.362415\pi$
$740$	−3.65063	−	6.32308i	−0.134200	−	0.232441i
$741$	−2.59640	+	27.7500i	−0.0953813	+	1.01942i
$742$	−9.59586	−	0.535634i	−0.352275	−	0.0196637i
$743$	−2.11279	+	7.88504i	−0.0775108	+	0.289274i	−0.993791	−	0.111264i	$-0.964510\pi$
$743$	−2.11279	+	7.88504i	−0.0775108	+	0.289274i	0.916280	+	0.400538i	$0.131177\pi$
$744$	4.07364	−	7.05576i	0.149347	−	0.258677i
$745$	4.11273	+	7.12345i	0.150679	+	0.260983i
$746$	−18.2999	+	4.90345i	−0.670008	+	0.179528i
$747$	−4.74859	+	4.74859i	−0.173742	+	0.173742i
$748$	−45.1227	+	12.0906i	−1.64985	+	0.442075i
$749$	26.0613	+	8.56596i	0.952260	+	0.312993i
$750$	−5.83086	+	10.0994i	−0.212913	+	0.368776i
$751$	−4.82305	−	2.78459i	−0.175995	−	0.101611i	0.409414	−	0.912349i	$-0.365733\pi$
$751$	−4.82305	−	2.78459i	−0.175995	−	0.101611i	−0.585410	+	0.810738i	$0.699066\pi$
$752$	−0.915942	−	0.915942i	−0.0334010	−	0.0334010i
$753$	17.9352	+	10.3549i	0.653596	+	0.377354i
$754$	−1.08063	+	11.5496i	−0.0393541	+	0.420611i
$755$			20.7190i			0.754040i
$756$	1.97219	−	1.76365i	0.0717277	−	0.0641435i
$757$	−15.2061	−	26.3377i	−0.552675	−	0.957262i	−0.998080	−	0.0619325i	$-0.980274\pi$
$757$	−15.2061	−	26.3377i	−0.552675	−	0.957262i	0.445405	−	0.895329i	$-0.353060\pi$
$758$			34.6020i			1.25680i
$759$	0.0973572	+	0.363342i	0.00353384	+	0.0131885i
$760$	−3.02401	+	11.2858i	−0.109692	+	0.409378i
$761$	−3.43260	−	3.43260i	−0.124432	−	0.124432i	0.642149	−	0.766580i	$-0.278043\pi$
$761$	−3.43260	−	3.43260i	−0.124432	−	0.124432i	−0.766580	+	0.642149i	$0.778043\pi$
$762$	−4.33060	−	4.33060i	−0.156881	−	0.156881i
$763$	16.7885	+	33.2281i	0.607783	+	1.20294i
$764$	−10.9386	+	6.31539i	−0.395744	+	0.228483i
$765$	2.93646	+	10.9590i	0.106168	+	0.396224i
$766$	−11.6330	+	20.1489i	−0.420316	+	0.728008i
$767$	32.6189	−	14.9718i	1.17780	−	0.540601i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−21.1806	−	5.67534i	−0.763794	−	0.204658i	−0.144166	−	0.989554i	$-0.546050\pi$
$769$	−21.1806	−	5.67534i	−0.763794	−	0.204658i	−0.619628	+	0.784896i	$0.712717\pi$
$770$	20.8261	+	13.6256i	0.750521	+	0.491032i
$771$	−8.23387	−	4.75383i	−0.296536	−	0.171205i
$772$	−0.513811	+	1.91757i	−0.0184925	+	0.0690149i
$773$	−2.56163	−	0.686385i	−0.0921353	−	0.0246876i	0.212457	−	0.977170i	$-0.431853\pi$
$773$	−2.56163	−	0.686385i	−0.0921353	−	0.0246876i	−0.304592	+	0.952483i	$0.598520\pi$
$774$	−4.29077	−	1.14971i	−0.154229	−	0.0413254i
$775$	−5.72592	+	21.3694i	−0.205681	+	0.767613i
$776$	−2.22075	−	1.28215i	−0.0797203	−	0.0460266i
$777$	−5.76340	−	11.4071i	−0.206761	−	0.409226i
$778$	−19.4286	−	5.20589i	−0.696550	−	0.186640i
$779$	−26.6696	+	15.3977i	−0.955537	+	0.551680i
$780$	3.15268	−	4.44524i	0.112884	−	0.159165i
$781$	1.60268	−	2.77592i	0.0573483	−	0.0993301i
$782$	−0.117426	−	0.438240i	−0.00419915	−	0.0156714i
$783$	2.78623	−	1.60863i	0.0995719	−	0.0574879i
$784$	−0.779042	+	6.95651i	−0.0278229	+	0.248447i
$785$	−23.8542	−	23.8542i	−0.851393	−	0.851393i
$786$	8.16716	+	8.16716i	0.291313	+	0.291313i
$787$	3.46034	−	12.9142i	0.123348	−	0.460340i	−0.876428	−	0.481534i	$-0.840080\pi$
$787$	3.46034	−	12.9142i	0.123348	−	0.460340i	0.999775	+	0.0211934i	$0.00674657\pi$
$788$	0.930208	+	3.47158i	0.0331373	+	0.123670i
$789$			17.8280i			0.634694i
$790$	8.66741	+	15.0124i	0.308373	+	0.534117i
$791$	−27.7790	−	9.13052i	−0.987707	−	0.324644i
$792$		−	6.22339i		−	0.221139i
$793$	2.30187	−	1.90798i	0.0817419	−	0.0677544i
$794$	−13.1120	−	7.57020i	−0.465327	−	0.268657i
$795$	3.88239	+	3.88239i	0.137694	+	0.137694i
$796$	8.82335	+	5.09416i	0.312735	+	0.180558i
$797$	−26.2340	+	45.4387i	−0.929257	+	1.60952i	−0.144689	+	0.989477i	$0.546218\pi$
$797$	−26.2340	+	45.4387i	−0.929257	+	1.60952i	−0.784568	+	0.620043i	$0.787115\pi$
$798$	−6.38610	+	19.4293i	−0.226065	+	0.687788i
$799$	9.39183	−	2.51653i	0.332259	−	0.0890286i
$800$	−1.92009	+	1.92009i	−0.0678854	+	0.0678854i
$801$	2.77244	−	0.742873i	0.0979593	−	0.0262481i
$802$	−9.47130	−	16.4048i	−0.334443	−	0.579272i
$803$	−25.3643	+	43.9322i	−0.895085	+	1.55033i
$804$	0.225277	−	0.840744i	0.00794490	−	0.0296508i
$805$	−0.132334	+	0.202267i	−0.00466417	+	0.00712899i
$806$	10.2132	−	27.5429i	0.359743	−	0.970156i
$807$	−4.57804	−	7.92939i	−0.161155	−	0.279128i
$808$	5.69662	−	5.69662i	0.200407	−	0.200407i
$809$	−5.45448			−0.191769			−0.0958846	−	0.995392i	$-0.530568\pi$
$809$	−5.45448			−0.191769			−0.0958846	+	0.995392i	$0.530568\pi$
$810$	−1.51148			−0.0531081
$811$	19.6603	−	19.6603i	0.690367	−	0.690367i	−0.271945	−	0.962313i	$-0.587667\pi$
$811$	19.6603	−	19.6603i	0.690367	−	0.690367i	0.962313	+	0.271945i	$0.0876670\pi$
$812$	−2.65790	+	8.08648i	−0.0932740	+	0.283780i
$813$	−4.40116	−	16.4254i	−0.154355	−	0.576062i
$814$	−29.0379	−	7.78069i	−1.01778	−	0.272713i
$815$	15.4553	−	8.92312i	0.541376	−	0.312563i
$816$			7.50626i			0.262772i
$817$	33.1680	−	8.88733i	1.16040	−	0.310928i
$818$	27.1980			0.950956
$819$	5.94364	−	7.46144i	0.207688	−	0.260724i
$820$	6.02152			0.210280
$821$	−37.7226	+	10.1077i	−1.31653	+	0.352763i	−0.847676	−	0.530514i	$-0.821999\pi$
$821$	−37.7226	+	10.1077i	−1.31653	+	0.352763i	−0.468852	+	0.883277i	$0.655332\pi$
$822$			4.24535i			0.148074i
$823$	−35.2498	+	20.3515i	−1.22873	+	0.709408i	−0.966765	−	0.255668i	$-0.917704\pi$
$823$	−35.2498	+	20.3515i	−1.22873	+	0.709408i	−0.261967	+	0.965077i	$0.584371\pi$
$824$	13.3822	+	3.58574i	0.466190	+	0.124915i
$825$	4.37381	+	16.3233i	0.152276	+	0.568303i
$826$	25.7796	−	5.38804i	0.896988	−	0.187474i
$827$	36.0061	−	36.0061i	1.25205	−	1.25205i	0.297257	−	0.954797i	$-0.403928\pi$
$827$	36.0061	−	36.0061i	1.25205	−	1.25205i	0.954797	−	0.297257i	$-0.0960718\pi$
$828$	0.0604428			0.00210053
$829$	26.4245			0.917761			0.458880	−	0.888498i	$-0.348251\pi$
$829$	26.4245			0.917761			0.458880	+	0.888498i	$0.348251\pi$
$830$	−7.17742	+	7.17742i	−0.249132	+	0.249132i
$831$	−5.76664	−	9.98812i	−0.200043	−	0.346484i
$832$	2.77593	−	2.30092i	0.0962380	−	0.0797700i
$833$	−42.2978	−	31.1730i	−1.46553	−	1.08008i
$834$	−2.25472	+	8.41475i	−0.0780747	+	0.291379i
$835$	−6.74893	+	11.6895i	−0.233556	+	0.404532i
$836$	24.0536	+	41.6621i	0.831913	+	1.44092i
$837$	−7.86967	+	2.10867i	−0.272016	+	0.0728864i
$838$	−5.17446	+	5.17446i	−0.178749	+	0.178749i
$839$	17.7480	−	4.75557i	0.612731	−	0.164181i	0.0609097	−	0.998143i	$-0.480600\pi$
$839$	17.7480	−	4.75557i	0.612731	−	0.164181i	0.551821	+	0.833963i	$0.313933\pi$
$840$	2.98093	−	2.66574i	0.102852	−	0.0919767i
$841$	9.32460	−	16.1507i	0.321538	−	0.556920i
$842$	−17.3942	−	10.0426i	−0.599444	−	0.346089i
$843$	10.6233	+	10.6233i	0.365887	+	0.365887i
$844$	22.0172	+	12.7116i	0.757863	+	0.437552i
$845$	8.51817	−	17.7069i	0.293034	−	0.609137i
$846$			1.29534i			0.0445346i
$847$	71.8165	−	15.0099i	2.46765	−	0.515748i
$848$	1.81627	+	3.14587i	0.0623709	+	0.108030i
$849$			12.0916i			0.414983i
$850$	−5.27541	−	19.6881i	−0.180945	−	0.675296i
$851$	0.0755676	−	0.282022i	0.00259042	−	0.00966759i
$852$	−0.364195	−	0.364195i	−0.0124771	−	0.0124771i
$853$	11.0707	+	11.0707i	0.379055	+	0.379055i	0.870761	−	0.491706i	$-0.163627\pi$
$853$	11.0707	+	11.0707i	0.379055	+	0.379055i	−0.491706	+	0.870761i	$0.663627\pi$
$854$	1.95818	−	0.989366i	0.0670075	−	0.0338554i
$855$	10.1185	−	5.84194i	0.346047	−	0.199790i
$856$	−2.68362	−	10.0154i	−0.0917241	−	0.342319i
$857$	−18.8859	+	32.7113i	−0.645128	+	1.11740i	0.339143	+	0.940735i	$0.389863\pi$
$857$	−18.8859	+	32.7113i	−0.645128	+	1.11740i	−0.984272	+	0.176661i	$0.943471\pi$
$858$	−3.76322	−	22.1209i	−0.128474	−	0.755197i
$859$	30.2113	−	17.4425i	1.03080	−	0.595131i	0.113585	−	0.993528i	$-0.463767\pi$
$859$	30.2113	−	17.4425i	1.03080	−	0.595131i	0.917213	+	0.398397i	$0.130433\pi$
$860$	−6.48543	−	1.73777i	−0.221151	−	0.0592574i
$861$	10.5239	+	0.587435i	0.358653	+	0.0200197i
$862$	2.72486	+	1.57320i	0.0928090	+	0.0535833i
$863$	−1.32222	+	4.93461i	−0.0450090	+	0.167976i	−0.984772	−	0.173851i	$-0.944379\pi$
$863$	−1.32222	+	4.93461i	−0.0450090	+	0.167976i	0.939763	+	0.341827i	$0.111046\pi$
$864$	−0.965926	−	0.258819i	−0.0328615	−	0.00880520i
$865$	32.3584	+	8.67042i	1.10022	+	0.294803i
$866$	−0.303724	+	1.13351i	−0.0103210	+	0.0385184i
$867$	−34.0729	−	19.6720i	−1.15718	−	0.668095i
$868$	11.8015	−	18.0381i	0.400569	−	0.612252i
$869$	68.9425	+	18.4731i	2.33871	+	0.626656i
$870$	4.21135	−	2.43142i	0.142778	−	0.0824330i
$871$	0.292354	−	3.12463i	0.00990603	−	0.105874i
$872$	7.03553	−	12.1859i	0.238253	−	0.412666i
$873$	0.663690	+	2.47693i	0.0224625	+	0.0838313i
$874$	−0.404631	+	0.233614i	−0.0136868	+	0.00790210i
$875$	−16.8922	+	25.8191i	−0.571062	+	0.872844i
$876$	5.76381	+	5.76381i	0.194741	+	0.194741i
$877$	23.8076	+	23.8076i	0.803925	+	0.803925i	0.983707	−	0.179781i	$-0.0575390\pi$
$877$	23.8076	+	23.8076i	0.803925	+	0.803925i	−0.179781	+	0.983707i	$0.557539\pi$
$878$	−7.24830	+	27.0510i	−0.244618	+	0.912928i
$879$	−2.01257	−	7.51103i	−0.0678824	−	0.253341i
$880$		−	9.40656i		−	0.317095i
$881$	−24.8501	−	43.0417i	−0.837223	−	1.45011i	−0.892208	−	0.451625i	$-0.850844\pi$
$881$	−24.8501	−	43.0417i	−0.837223	−	1.45011i	0.0549851	−	0.998487i	$-0.482489\pi$
$882$	5.46986	−	4.36813i	0.184180	−	0.147083i
$883$			3.25270i			0.109462i	0.998501	+	0.0547310i	$0.0174301\pi$
$883$			3.25270i			0.109462i	−0.998501	+	0.0547310i	$0.982570\pi$
$884$	4.53895	+	26.6809i	0.152661	+	0.897375i
$885$	−13.0300	−	7.52290i	−0.438000	−	0.252880i
$886$	−10.2910	−	10.2910i	−0.345734	−	0.345734i
$887$	−25.9193	−	14.9645i	−0.870284	−	0.502459i	−0.00284144	−	0.999996i	$-0.500904\pi$
$887$	−25.9193	−	14.9645i	−0.870284	−	0.502459i	−0.867443	+	0.497537i	$0.834238\pi$
$888$	−2.41526	+	4.18336i	−0.0810509	+	0.140384i
$889$	−10.8013	−	12.0784i	−0.362264	−	0.405098i
$890$	4.19050	−	1.12284i	0.140466	−	0.0376377i
$891$	−4.40060	+	4.40060i	−0.147426	+	0.147426i
$892$	−10.2954	+	2.75865i	−0.344716	+	0.0923664i
$893$	−5.00653	−	8.67156i	−0.167537	−	0.290183i
$894$	2.72099	−	4.71289i	0.0910034	−	0.157622i
$895$	−3.84726	+	14.3582i	−0.128600	+	0.479941i
$896$	2.36145	−	1.19312i	0.0788906	−	0.0398594i
$897$	0.214843	−	0.0365491i	0.00717340	−	0.00122034i
$898$	16.5111	+	28.5981i	0.550982	+	0.954329i
$899$	18.5347	−	18.5347i	0.618166	−	0.618166i
$900$	2.71542			0.0905138
$901$	−27.2668			−0.908388
$902$	17.5313	−	17.5313i	0.583729	−	0.583729i
$903$	−11.1651	−	3.66981i	−0.371553	−	0.122124i
$904$	2.86049	+	10.6755i	0.0951384	+	0.355061i
$905$	−16.5226	−	4.42722i	−0.549231	−	0.147166i
$906$	11.8712	−	6.85385i	0.394395	−	0.227704i
$907$			41.0812i			1.36408i	0.731316	+	0.682039i	$0.238906\pi$
$907$			41.0812i			1.36408i	−0.731316	+	0.682039i	$0.761094\pi$
$908$	2.56781	−	0.688042i	0.0852157	−	0.0228335i
$909$	−8.05624			−0.267209
$910$	8.98372	−	11.2779i	0.297808	−	0.373857i
$911$	42.9297			1.42232			0.711162	−	0.703028i	$-0.248169\pi$
$911$	42.9297			1.42232			0.711162	+	0.703028i	$0.248169\pi$
$912$	7.46668	−	2.00069i	0.247246	−	0.0662495i
$913$			41.7934i			1.38316i
$914$	−20.3332	+	11.7394i	−0.672564	+	0.388305i
$915$	−1.21065	−	0.324394i	−0.0400230	−	0.0107241i
$916$	−0.650085	−	2.42615i	−0.0214794	−	0.0801622i
$917$	20.3704	+	22.7790i	0.672690	+	0.752228i
$918$	5.30773	−	5.30773i	0.175181	−	0.175181i
$919$	40.4685			1.33493			0.667466	−	0.744640i	$-0.267379\pi$
$919$	40.4685			1.33493			0.667466	+	0.744640i	$0.267379\pi$
$920$	0.0913583			0.00301200
$921$	0.870087	−	0.870087i	0.0286704	−	0.0286704i
$922$	−14.7946	−	25.6251i	−0.487235	−	0.843916i
$923$	−1.51475	−	1.07430i	−0.0498585	−	0.0353610i
$924$	0.917667	−	16.4400i	0.0301890	−	0.540835i
$925$	3.39490	−	12.6699i	0.111624	−	0.416585i
$926$	−10.7060	+	18.5433i	−0.351820	+	0.609371i
$927$	−6.92712	−	11.9981i	−0.227516	−	0.394070i
$928$	3.10764	−	0.832690i	0.102013	−	0.0273344i
$929$	−30.1896	+	30.1896i	−0.990490	+	0.990490i	−0.999955	−	0.00946507i	$-0.996987\pi$
$929$	−30.1896	+	30.1896i	−0.990490	+	0.990490i	0.00946507	+	0.999955i	$0.496987\pi$
$930$	−11.8949	+	3.18723i	−0.390049	+	0.104513i
$931$	−19.7347	+	50.3834i	−0.646778	+	1.65125i
$932$	10.2191	−	17.7000i	0.334738	−	0.579783i
$933$	−15.5505	−	8.97807i	−0.509100	−	0.293929i
$934$	−20.4912	−	20.4912i	−0.670493	−	0.670493i
$935$	61.1484	+	35.3041i	1.99977	+	1.15457i
$936$	−3.58987	−	0.335884i	−0.117339	−	0.0109787i
$937$		−	20.8141i		−	0.679967i	−0.940431	−	0.339984i	$-0.889578\pi$
$937$		−	20.8141i		−	0.679967i	0.940431	−	0.339984i	$-0.110422\pi$
$938$	0.719071	−	2.18772i	0.0234785	−	0.0714317i
$939$	0.232688	+	0.403027i	0.00759347	+	0.0131523i
$940$			1.95788i			0.0638591i
$941$	3.84739	+	14.3586i	0.125421	+	0.468078i	0.999854	−	0.0170677i	$-0.00543308\pi$
$941$	3.84739	+	14.3586i	0.125421	+	0.468078i	−0.874433	+	0.485146i	$0.838766\pi$
$942$	−5.77660	+	21.5586i	−0.188212	+	0.702416i
$943$	0.170267	+	0.170267i	0.00554467	+	0.00554467i
$944$	−7.03877	−	7.03877i	−0.229092	−	0.229092i
$945$	−3.99280	−	0.222875i	−0.129886	−	0.00725012i
$946$	−23.9414	+	13.8226i	−0.778402	+	0.449411i
$947$	−2.82217	−	10.5325i	−0.0917082	−	0.342259i	0.904792	−	0.425855i	$-0.140026\pi$
$947$	−2.82217	−	10.5325i	−0.0917082	−	0.342259i	−0.996500	+	0.0835950i	$0.973360\pi$
$948$	5.73437	−	9.93222i	0.186244	−	0.322584i
$949$	23.9727	+	17.0021i	0.778187	+	0.551910i
$950$	−18.1782	+	10.4952i	−0.589778	+	0.340509i
$951$	−0.157858	−	0.0422978i	−0.00511889	−	0.00137160i
$952$	−1.10683	+	19.8288i	−0.0358726	+	0.642656i
$953$	−2.68793	−	1.55188i	−0.0870707	−	0.0502703i	0.455832	−	0.890066i	$-0.349342\pi$
$953$	−2.68793	−	1.55188i	−0.0870707	−	0.0502703i	−0.542903	+	0.839795i	$0.682675\pi$
$954$	0.940170	−	3.50876i	0.0304391	−	0.113600i
$955$	18.4407	+	4.94118i	0.596728	+	0.159893i
$956$	−16.5194	−	4.42637i	−0.534277	−	0.143159i
$957$	5.18216	−	19.3401i	0.167515	−	0.625176i
$958$	−25.4257	−	14.6796i	−0.821468	−	0.474275i
$959$	−0.625995	+	11.2147i	−0.0202144	+	0.362141i
$960$	−1.45998	−	0.391201i	−0.0471207	−	0.0126260i
$961$	−30.6385	+	17.6891i	−0.988338	+	0.570617i
$962$	−6.05538	+	16.3302i	−0.195233	+	0.526506i
$963$	−5.18435	+	8.97955i	−0.167063	+	0.289362i
$964$	1.73894	+	6.48980i	0.0560074	+	0.209023i
$965$	2.59861	−	1.50031i	0.0836524	−	0.0482967i
$966$	0.159668	+	0.00891256i	0.00513724	+	0.000286757i
$967$	−22.1771	−	22.1771i	−0.713169	−	0.713169i	0.254028	−	0.967197i	$-0.418244\pi$
$967$	−22.1771	−	22.1771i	−0.713169	−	0.713169i	−0.967197	+	0.254028i	$0.918244\pi$
$968$	−19.6085	−	19.6085i	−0.630242	−	0.630242i
$969$	−15.0177	+	56.0468i	−0.482438	+	1.80048i
$970$	1.00316	+	3.74384i	0.0322095	+	0.120207i
$971$			29.5052i			0.946866i	0.880830	+	0.473433i	$0.156985\pi$
$971$			29.5052i			0.946866i	−0.880830	+	0.473433i	$0.843015\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−7.19696	+	21.8963i	−0.230724	+	0.701962i
$974$		−	28.7439i		−	0.921013i
$975$	9.65190	−	1.64198i	0.309108	−	0.0525855i
$976$	−0.718131	−	0.414613i	−0.0229868	−	0.0132714i
$977$	0.751293	+	0.751293i	0.0240360	+	0.0240360i	0.719023	−	0.694987i	$-0.244590\pi$
$977$	0.751293	+	0.751293i	0.0240360	+	0.0240360i	−0.694987	+	0.719023i	$0.744590\pi$
$978$	−10.2252	−	5.90355i	−0.326967	−	0.188775i
$979$	8.93132	−	15.4695i	0.285446	−	0.494407i
$980$	8.26761	−	6.60236i	0.264099	−	0.210905i
$981$	−13.5916	+	3.64186i	−0.433946	+	0.116276i
$982$	22.6864	−	22.6864i	0.723953	−	0.723953i
$983$	6.71970	−	1.80054i	0.214325	−	0.0574282i	−0.150059	−	0.988677i	$-0.547946\pi$
$983$	6.71970	−	1.80054i	0.214325	−	0.0574282i	0.364384	+	0.931249i	$0.381280\pi$
$984$	−1.99192	−	3.45011i	−0.0635001	−	0.109985i
$985$	2.71617	−	4.70455i	0.0865445	−	0.149899i
$986$	−6.25039	+	23.3268i	−0.199053	+	0.742875i
$987$	−0.191003	+	3.42181i	−0.00607970	+	0.108918i
$988$	25.3304	−	11.6264i	0.805867	−	0.369886i
$989$	−0.134247	−	0.232523i	−0.00426882	−	0.00739382i
$990$	−6.65144	+	6.65144i	−0.211397	+	0.211397i
$991$	−18.8206			−0.597855			−0.298928	−	0.954276i	$-0.596629\pi$
$991$	−18.8206			−0.597855			−0.298928	+	0.954276i	$0.596629\pi$
$992$	−8.14729			−0.258677
$993$	8.31583	−	8.31583i	0.263895	−	0.263895i
$994$	−0.908369	−	1.01577i	−0.0288117	−	0.0322184i
$995$	−3.98568	−	14.8748i	−0.126355	−	0.471562i
$996$	6.48670	+	1.73811i	0.205539	+	0.0550740i
$997$	4.97512	−	2.87239i	0.157564	−	0.0909694i	−0.419145	−	0.907919i	$-0.637670\pi$
$997$	4.97512	−	2.87239i	0.157564	−	0.0909694i	0.576709	+	0.816950i	$0.304337\pi$
$998$		−	3.33021i		−	0.105416i
$999$	4.66593	−	1.25023i	0.147624	−	0.0395556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.115.8	yes	40
7.5	odd	6		546.2.cg.b.271.3	yes	40
13.6	odd	12		546.2.cg.b.409.3	yes	40
91.19	even	12	inner	546.2.by.b.19.8	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.8	✓	40	91.19	even	12	inner
546.2.by.b.115.8	yes	40	1.1	even	1	trivial
546.2.cg.b.271.3	yes	40	7.5	odd	6
546.2.cg.b.409.3	yes	40	13.6	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.45998 - 0.391201i) q^{5} +(0.258819 + 0.965926i) q^{6} +(0.541277 + 2.58979i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.45998 - 0.391201i) q^{5} +(0.258819 + 0.965926i) q^{6} +(0.541277 + 2.58979i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -1.51148 q^{10} +(-4.40060 + 4.40060i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.30092 + 2.77593i) q^{13} +(1.19312 + 2.36145i) q^{14} +(0.391201 - 1.45998i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.75313 + 6.50061i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(5.46599 - 5.46599i) q^{19} +(-1.45998 + 0.391201i) q^{20} +(-2.58979 + 0.541277i) q^{21} +(-3.11170 + 5.38962i) q^{22} +(-0.0523450 - 0.0302214i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-2.35162 - 1.35771i) q^{25} +(2.94098 + 2.08582i) q^{26} -1.00000i q^{27} +(1.76365 + 1.97219i) q^{28} +(1.60863 + 2.78623i) q^{29} -1.51148i q^{30} +(-2.10867 - 7.86967i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-4.40060 - 4.40060i) q^{33} +(5.30773 + 5.30773i) q^{34} +(0.222875 - 3.99280i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(1.25023 + 4.66593i) q^{37} +(3.86504 - 6.69444i) q^{38} +(-2.77593 + 2.30092i) q^{39} +(-1.30898 + 0.755742i) q^{40} +(-3.84810 - 1.03109i) q^{41} +(-2.36145 + 1.19312i) q^{42} +(3.84700 + 2.22107i) q^{43} +(-1.61073 + 6.01134i) q^{44} +(1.45998 + 0.391201i) q^{45} +(-0.0583833 - 0.0156437i) q^{46} +(0.335258 - 1.25120i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-6.41404 + 2.80359i) q^{49} +(-2.62289 - 0.702801i) q^{50} +(-6.50061 + 3.75313i) q^{51} +(3.38062 + 1.25357i) q^{52} +(-1.81627 + 3.14587i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(8.14632 - 4.70328i) q^{55} +(2.21400 + 1.44852i) q^{56} +(5.46599 + 5.46599i) q^{57} +(2.27495 + 2.27495i) q^{58} +(2.57637 - 9.61514i) q^{59} +(-0.391201 - 1.45998i) q^{60} -0.829226i q^{61} +(-4.07364 - 7.05576i) q^{62} +(-0.541277 - 2.58979i) q^{63} -1.00000i q^{64} +(-2.27335 - 4.95293i) q^{65} +(-5.38962 - 3.11170i) q^{66} +(-0.615467 - 0.615467i) q^{67} +(6.50061 + 3.75313i) q^{68} +(0.0302214 - 0.0523450i) q^{69} +(-0.818131 - 3.91443i) q^{70} +(-0.497499 + 0.133304i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(7.87352 - 2.10970i) q^{73} +(2.41526 + 4.18336i) q^{74} +(1.35771 - 2.35162i) q^{75} +(2.00069 - 7.46668i) q^{76} +(-13.7786 - 9.01470i) q^{77} +(-2.08582 + 2.94098i) q^{78} +(-5.73437 - 9.93222i) q^{79} +(-1.06878 + 1.06878i) q^{80} +1.00000 q^{81} -3.98384 q^{82} +(4.74859 - 4.74859i) q^{83} +(-1.97219 + 1.76365i) q^{84} +(-2.93646 - 10.9590i) q^{85} +(4.29077 + 1.14971i) q^{86} +(-2.78623 + 1.60863i) q^{87} +6.22339i q^{88} +(-2.77244 + 0.742873i) q^{89} +1.51148 q^{90} +(-5.94364 + 7.46144i) q^{91} -0.0604428 q^{92} +(7.86967 - 2.10867i) q^{93} -1.29534i q^{94} +(-10.1185 + 5.84194i) q^{95} +(0.965926 + 0.258819i) q^{96} +(-0.663690 - 2.47693i) q^{97} +(-5.46986 + 4.36813i) q^{98} +(4.40060 - 4.40060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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