LMFDB - Embedded newform 546.2.cg.b.409.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (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			409.3
Character	$\chi$	$=$	546.409
Dual form			546.2.cg.b.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.391201 + 1.45998i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.826136 - 2.51346i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.391201 + 1.45998i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.826136 - 2.51346i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.755742 - 1.30898i) q^{10} +(-1.61073 + 6.01134i) 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} -1.00000 q^{16} +7.50626 q^{17} +(0.258819 + 0.965926i) q^{18} +(7.46668 - 2.00069i) q^{19} +(1.45998 + 0.391201i) q^{20} +(-0.541277 - 2.58979i) q^{21} +(-3.11170 - 5.38962i) q^{22} -0.0604428i q^{23} +(0.965926 + 0.258819i) q^{24} +(2.35162 + 1.35771i) q^{25} +(-0.335884 - 3.58987i) q^{26} -1.00000i q^{27} +(-2.51346 - 0.826136i) q^{28} +(1.60863 - 2.78623i) q^{29} +(-1.30898 - 0.755742i) q^{30} +(-7.86967 + 2.10867i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.61073 + 6.01134i) q^{33} +(-5.30773 + 5.30773i) q^{34} +(3.34643 + 2.18941i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(3.41570 + 3.41570i) q^{37} +(-3.86504 + 6.69444i) q^{38} +(-0.604689 + 3.55448i) q^{39} +(-1.30898 + 0.755742i) q^{40} +(3.84810 - 1.03109i) q^{41} +(2.21400 + 1.44852i) q^{42} +(3.84700 - 2.22107i) q^{43} +(6.01134 + 1.61073i) q^{44} +(1.06878 + 1.06878i) q^{45} +(0.0427395 + 0.0427395i) q^{46} +(1.25120 + 0.335258i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-5.63500 - 4.15293i) q^{49} +(-2.62289 + 0.702801i) q^{50} +(6.50061 - 3.75313i) q^{51} +(2.77593 + 2.30092i) q^{52} +(-1.81627 + 3.14587i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-8.14632 - 4.70328i) q^{55} +(2.36145 - 1.19312i) q^{56} +(5.46599 - 5.46599i) q^{57} +(0.832690 + 3.10764i) q^{58} +(-7.03877 + 7.03877i) q^{59} +(1.45998 - 0.391201i) q^{60} +(0.718131 + 0.414613i) q^{61} +(4.07364 - 7.05576i) q^{62} +(-1.76365 - 1.97219i) q^{63} +1.00000i q^{64} +(-3.15268 - 4.44524i) q^{65} +(-5.38962 - 3.11170i) q^{66} +(0.840744 + 0.225277i) q^{67} -7.50626i q^{68} +(-0.0302214 - 0.0523450i) q^{69} +(-3.91443 + 0.818131i) q^{70} +(-0.497499 - 0.133304i) q^{71} +(0.965926 - 0.258819i) q^{72} +(2.10970 + 7.87352i) q^{73} -4.83053 q^{74} +2.71542 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} +(0.391201 - 1.45998i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.99192 + 3.45011i) q^{82} +(-4.74859 - 4.74859i) q^{83} +(-2.58979 + 0.541277i) q^{84} +(-2.93646 + 10.9590i) q^{85} +(-1.14971 + 4.29077i) q^{86} -3.21727i q^{87} +(-5.38962 + 3.11170i) q^{88} +(-2.02957 + 2.02957i) q^{89} -1.51148 q^{90} +(5.07632 + 8.07657i) q^{91} -0.0604428 q^{92} +(-5.76100 + 5.76100i) q^{93} +(-1.12180 + 0.647669i) q^{94} +11.6839i q^{95} +(0.258819 - 0.965926i) q^{96} +(0.663690 - 2.47693i) q^{97} +(6.92111 - 1.04798i) q^{98} +(4.40060 + 4.40060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	−0.391201	+	1.45998i	−0.174950	+	0.652924i	0.821610	+	0.570050i	$0.193076\pi$
$5$	−0.391201	+	1.45998i	−0.174950	+	0.652924i	−0.996560	+	0.0828733i	$0.973590\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	0.826136	−	2.51346i	0.312250	−	0.950000i
$7$	0.826136	−	2.51346i	0.312250	−	0.950000i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.755742	−	1.30898i	−0.238987	−	0.413937i
$11$	−1.61073	+	6.01134i	−0.485654	+	1.81249i	0.0914424	+	0.995810i	$0.470852\pi$
$11$	−1.61073	+	6.01134i	−0.485654	+	1.81249i	−0.577097	+	0.816676i	$0.695814\pi$
$12$	−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
$16$	−1.00000			−0.250000
$17$	7.50626			1.82054			0.910268	−	0.414020i	$-0.135876\pi$
$17$	7.50626			1.82054			0.910268	+	0.414020i	$0.135876\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	7.46668	−	2.00069i	1.71297	−	0.458990i	0.736823	−	0.676085i	$-0.236325\pi$
$19$	7.46668	−	2.00069i	1.71297	−	0.458990i	0.976150	+	0.217096i	$0.0696583\pi$
$20$	1.45998	+	0.391201i	0.326462	+	0.0874752i
$21$	−0.541277	−	2.58979i	−0.118116	−	0.565139i
$22$	−3.11170	−	5.38962i	−0.663416	−	1.14907i
$23$		−	0.0604428i		−	0.0126032i	−0.999980	−	0.00630160i	$-0.997994\pi$
$23$		−	0.0604428i		−	0.0126032i	0.999980	−	0.00630160i	$-0.00200587\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$	2.35162	+	1.35771i	0.470324	+	0.271542i
$26$	−0.335884	−	3.58987i	−0.0658722	−	0.704032i
$27$		−	1.00000i		−	0.192450i
$28$	−2.51346	−	0.826136i	−0.475000	−	0.156125i
$29$	1.60863	−	2.78623i	0.298716	−	0.517391i	−0.677127	−	0.735866i	$-0.736775\pi$
$29$	1.60863	−	2.78623i	0.298716	−	0.517391i	0.975842	+	0.218476i	$0.0701085\pi$
$30$	−1.30898	−	0.755742i	−0.238987	−	0.137979i
$31$	−7.86967	+	2.10867i	−1.41344	+	0.378729i	−0.883150	−	0.469091i	$-0.844582\pi$
$31$	−7.86967	+	2.10867i	−1.41344	+	0.378729i	−0.530285	+	0.847819i	$0.677915\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.61073	+	6.01134i	0.280393	+	1.04644i
$34$	−5.30773	+	5.30773i	−0.910268	+	0.910268i
$35$	3.34643	+	2.18941i	0.565649	+	0.370078i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	3.41570	+	3.41570i	0.561537	+	0.561537i	0.929744	−	0.368207i	$-0.120028\pi$
$37$	3.41570	+	3.41570i	0.561537	+	0.561537i	−0.368207	+	0.929744i	$0.620028\pi$
$38$	−3.86504	+	6.69444i	−0.626992	+	1.08598i
$39$	−0.604689	+	3.55448i	−0.0968277	+	0.569173i
$40$	−1.30898	+	0.755742i	−0.206969	+	0.119493i
$41$	3.84810	−	1.03109i	0.600972	−	0.161030i	0.0545089	−	0.998513i	$-0.482641\pi$
$41$	3.84810	−	1.03109i	0.600972	−	0.161030i	0.546463	+	0.837483i	$0.315974\pi$
$42$	2.21400	+	1.44852i	0.341628	+	0.223511i
$43$	3.84700	−	2.22107i	0.586662	−	0.338709i	−0.177114	−	0.984190i	$-0.556676\pi$
$43$	3.84700	−	2.22107i	0.586662	−	0.338709i	0.763777	+	0.645481i	$0.223343\pi$
$44$	6.01134	+	1.61073i	0.906243	+	0.242827i
$45$	1.06878	+	1.06878i	0.159324	+	0.159324i
$46$	0.0427395	+	0.0427395i	0.00630160	+	0.00630160i
$47$	1.25120	+	0.335258i	0.182506	+	0.0489024i	0.348915	−	0.937155i	$-0.386550\pi$
$47$	1.25120	+	0.335258i	0.182506	+	0.0489024i	−0.166408	+	0.986057i	$0.553217\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−5.63500	−	4.15293i	−0.805000	−	0.593275i
$50$	−2.62289	+	0.702801i	−0.370933	+	0.0993911i
$51$	6.50061	−	3.75313i	0.910268	−	0.525543i
$52$	2.77593	+	2.30092i	0.384952	+	0.319080i
$53$	−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	$0.246928\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−8.14632	−	4.70328i	−1.09845	−	0.634190i
$56$	2.36145	−	1.19312i	0.315563	−	0.159437i
$57$	5.46599	−	5.46599i	0.723988	−	0.723988i
$58$	0.832690	+	3.10764i	0.109338	+	0.408053i
$59$	−7.03877	+	7.03877i	−0.916370	+	0.916370i	−0.996763	−	0.0803936i	$-0.974382\pi$
$59$	−7.03877	+	7.03877i	−0.916370	+	0.916370i	0.0803936	+	0.996763i	$0.474382\pi$
$60$	1.45998	−	0.391201i	0.188483	−	0.0505038i
$61$	0.718131	+	0.414613i	0.0919472	+	0.0530858i	0.545269	−	0.838261i	$-0.316428\pi$
$61$	0.718131	+	0.414613i	0.0919472	+	0.0530858i	−0.453321	+	0.891347i	$0.649761\pi$
$62$	4.07364	−	7.05576i	0.517353	−	0.896082i
$63$	−1.76365	−	1.97219i	−0.222200	−	0.248472i
$64$			1.00000i			0.125000i
$65$	−3.15268	−	4.44524i	−0.391042	−	0.551365i
$66$	−5.38962	−	3.11170i	−0.663416	−	0.383023i
$67$	0.840744	+	0.225277i	0.102713	+	0.0275219i	0.309810	−	0.950799i	$-0.399735\pi$
$67$	0.840744	+	0.225277i	0.102713	+	0.0275219i	−0.207096	+	0.978321i	$0.566401\pi$
$68$		−	7.50626i		−	0.910268i
$69$	−0.0302214	−	0.0523450i	−0.00363823	−	0.00630160i
$70$	−3.91443	+	0.818131i	−0.467864	+	0.0977854i
$71$	−0.497499	−	0.133304i	−0.0590423	−	0.0158203i	0.229177	−	0.973385i	$-0.426397\pi$
$71$	−0.497499	−	0.133304i	−0.0590423	−	0.0158203i	−0.288219	+	0.957564i	$0.593063\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	2.10970	+	7.87352i	0.246922	+	0.921525i	0.972408	+	0.233288i	$0.0749485\pi$
$73$	2.10970	+	7.87352i	0.246922	+	0.921525i	−0.725486	+	0.688237i	$0.758385\pi$
$74$	−4.83053			−0.561537
$75$	2.71542			0.313549
$76$	−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	$-0.389879\pi$
$80$	0.391201	−	1.45998i	0.0437376	−	0.163231i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.99192	+	3.45011i	−0.219971	+	0.381001i
$83$	−4.74859	−	4.74859i	−0.521226	−	0.521226i	0.396716	−	0.917942i	$-0.370150\pi$
$83$	−4.74859	−	4.74859i	−0.521226	−	0.521226i	−0.917942	+	0.396716i	$0.870150\pi$
$84$	−2.58979	+	0.541277i	−0.282569	+	0.0590581i
$85$	−2.93646	+	10.9590i	−0.318503	+	1.18867i
$86$	−1.14971	+	4.29077i	−0.123976	+	0.462686i
$87$		−	3.21727i		−	0.344927i
$88$	−5.38962	+	3.11170i	−0.574535	+	0.331708i
$89$	−2.02957	+	2.02957i	−0.215134	+	0.215134i	−0.806444	−	0.591310i	$-0.798611\pi$
$89$	−2.02957	+	2.02957i	−0.215134	+	0.215134i	0.591310	+	0.806444i	$0.298611\pi$
$90$	−1.51148			−0.159324
$91$	5.07632	+	8.07657i	0.532143	+	0.846654i
$92$	−0.0604428			−0.00630160
$93$	−5.76100	+	5.76100i	−0.597388	+	0.597388i
$94$	−1.12180	+	0.647669i	−0.115704	+	0.0668019i
$95$			11.6839i			1.19874i
$96$	0.258819	−	0.965926i	0.0264156	−	0.0985844i
$97$	0.663690	−	2.47693i	0.0673876	−	0.251494i	−0.924012	−	0.382363i	$-0.875110\pi$
$97$	0.663690	−	2.47693i	0.0673876	−	0.251494i	0.991400	+	0.130870i	$0.0417769\pi$
$98$	6.92111	−	1.04798i	0.699137	−	0.105862i
$99$	4.40060	+	4.40060i	0.442277	+	0.442277i
$100$	1.35771	−	2.35162i	0.135771	−	0.235162i
$101$	4.02812	+	6.97691i	0.400813	+	0.694229i	0.993824	−	0.110966i	$-0.0353943\pi$
$101$	4.02812	+	6.97691i	0.400813	+	0.694229i	−0.593011	+	0.805194i	$0.702061\pi$
$102$	−1.94276	+	7.25049i	−0.192362	+	0.717906i
$103$	−6.92712	−	11.9981i	−0.682549	−	1.18221i	−0.974200	−	0.225685i	$-0.927538\pi$
$103$	−6.92712	−	11.9981i	−0.682549	−	1.18221i	0.291651	−	0.956525i	$-0.405795\pi$
$104$	−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
$107$	−10.3687			−1.00238			−0.501190	−	0.865337i	$-0.667104\pi$
$107$	−10.3687			−1.00238			−0.501190	+	0.865337i	$0.667104\pi$
$108$	−1.00000			−0.0962250
$109$	−3.64186	−	13.5916i	−0.348827	−	1.30184i	−0.888078	−	0.459693i	$-0.847959\pi$
$109$	−3.64186	−	13.5916i	−0.348827	−	1.30184i	0.539251	−	0.842145i	$-0.318707\pi$
$110$	9.08604	−	2.43460i	0.866320	−	0.232130i
$111$	4.66593	+	1.25023i	0.442871	+	0.118667i
$112$	−0.826136	+	2.51346i	−0.0780626	+	0.237500i
$113$	−5.52604	−	9.57138i	−0.519846	−	0.900400i	−0.999734	−	0.0230698i	$-0.992656\pi$
$113$	−5.52604	−	9.57138i	−0.519846	−	0.900400i	0.479888	−	0.877330i	$-0.340677\pi$
$114$			7.73007i			0.723988i
$115$	0.0882454	+	0.0236453i	0.00822892	+	0.00220493i
$116$	−2.78623	−	1.60863i	−0.258695	−	0.149358i
$117$	1.25357	+	3.38062i	0.115892	+	0.312538i
$118$		−	9.95432i		−	0.916370i
$119$	6.20120	−	18.8667i	0.568463	−	1.72951i
$120$	−0.755742	+	1.30898i	−0.0689895	+	0.119493i
$121$	−24.0154	−	13.8653i	−2.18322	−	1.26048i
$122$	−0.800971	+	0.214619i	−0.0725165	+	0.0194307i
$123$	2.81700	−	2.81700i	0.254001	−	0.254001i
$124$	2.10867	+	7.86967i	0.189364	+	0.706718i
$125$	−8.24609	+	8.24609i	−0.737553	+	0.737553i
$126$	2.64164	+	0.147454i	0.235336	+	0.0131363i
$127$	−5.30387	−	3.06219i	−0.470643	−	0.271726i	0.245866	−	0.969304i	$-0.420928\pi$
$127$	−5.30387	−	3.06219i	−0.470643	−	0.271726i	−0.716509	+	0.697578i	$0.754261\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	2.22107	−	3.84700i	0.195554	−	0.338709i
$130$	5.37255	+	0.913978i	0.471203	+	0.0801611i
$131$	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
$133$	1.13983	−	20.4201i	0.0988361	−	1.77064i
$134$	−0.753791	+	0.435201i	−0.0651176	+	0.0375957i
$135$	1.45998	+	0.391201i	0.125655	+	0.0336692i
$136$	5.30773	+	5.30773i	0.455134	+	0.455134i
$137$	−3.00191	−	3.00191i	−0.256471	−	0.256471i	0.567146	−	0.823617i	$-0.308047\pi$
$137$	−3.00191	−	3.00191i	−0.256471	−	0.256471i	−0.823617	+	0.567146i	$0.808047\pi$
$138$	0.0583833	+	0.0156437i	0.00496991	+	0.00133168i
$139$	−7.54445	+	4.35579i	−0.639912	+	0.369454i	−0.784581	−	0.620027i	$-0.787122\pi$
$139$	−7.54445	+	4.35579i	−0.639912	+	0.369454i	0.144668	+	0.989480i	$0.453788\pi$
$140$	2.18941	−	3.34643i	0.185039	−	0.282825i
$141$	1.25120	−	0.335258i	0.105370	−	0.0282338i
$142$	0.446045	−	0.257524i	0.0374313	−	0.0216110i
$143$	−12.9809	−	18.3029i	−1.08552	−	1.53056i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	3.43855	+	3.43855i	0.285556	+	0.285556i
$146$	−7.05920	−	4.07563i	−0.584224	−	0.337302i
$147$	−6.95651	−	0.779042i	−0.573764	−	0.0642543i
$148$	3.41570	−	3.41570i	0.280769	−	0.280769i
$149$	−1.40849	−	5.25654i	−0.115388	−	0.430633i	0.883928	−	0.467623i	$-0.154890\pi$
$149$	−1.40849	−	5.25654i	−0.115388	−	0.430633i	−0.999316	+	0.0369905i	$0.988223\pi$
$150$	−1.92009	+	1.92009i	−0.156775	+	0.156775i
$151$	13.2406	−	3.54781i	1.07751	−	0.288717i	0.323932	−	0.946080i	$-0.394995\pi$
$151$	13.2406	−	3.54781i	1.07751	−	0.288717i	0.753574	+	0.657363i	$0.228328\pi$
$152$	6.69444	+	3.86504i	0.542991	+	0.313496i
$153$	3.75313	−	6.50061i	0.303423	−	0.525543i
$154$	−16.1173	+	3.36858i	−1.29877	+	0.271448i
$155$		−	12.3145i		−	0.989124i
$156$	3.55448	+	0.604689i	0.284586	+	0.0484138i
$157$	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	$0.316932\pi$
$158$	11.0780	+	2.96833i	0.881315	+	0.236148i
$159$			3.63254i			0.288079i
$160$	0.755742	+	1.30898i	0.0597467	+	0.103484i
$161$	−0.151921	−	0.0499340i	−0.0119730	−	0.00393535i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	11.4048	−	3.05590i	0.893292	−	0.239357i	0.217159	−	0.976136i	$-0.430321\pi$
$163$	11.4048	−	3.05590i	0.893292	−	0.239357i	0.676133	+	0.736780i	$0.263654\pi$
$164$	−1.03109	−	3.84810i	−0.0805149	−	0.300486i
$165$	−9.40656			−0.732300
$166$	6.71552			0.521226
$167$	−2.31131	−	8.62592i	−0.178854	−	0.667493i	−0.995863	−	0.0908680i	$-0.971036\pi$
$167$	−2.31131	−	8.62592i	−0.178854	−	0.667493i	0.817009	−	0.576625i	$-0.195631\pi$
$168$	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
$171$	2.00069	−	7.46668i	0.152997	−	0.570991i
$172$	−2.22107	−	3.84700i	−0.169355	−	0.293331i
$173$	−11.0818	+	19.1942i	−0.842533	+	1.45931i	0.0452133	+	0.998977i	$0.485603\pi$
$173$	−11.0818	+	19.1942i	−0.842533	+	1.45931i	−0.887746	+	0.460333i	$0.847730\pi$
$174$	2.27495	+	2.27495i	0.172464	+	0.172464i
$175$	5.35531	−	4.78906i	0.404823	−	0.362019i
$176$	1.61073	−	6.01134i	0.121414	−	0.453122i
$177$	−2.57637	+	9.61514i	−0.193652	+	0.722718i
$178$		−	2.87024i		−	0.215134i
$179$	8.51691	−	4.91724i	0.636584	−	0.367532i	−0.146713	−	0.989179i	$-0.546870\pi$
$179$	8.51691	−	4.91724i	0.636584	−	0.367532i	0.783297	+	0.621647i	$0.213536\pi$
$180$	1.06878	−	1.06878i	0.0796622	−	0.0796622i
$181$	−11.3170			−0.841186			−0.420593	−	0.907249i	$-0.638178\pi$
$181$	−11.3170			−0.841186			−0.420593	+	0.907249i	$0.638178\pi$
$182$	−9.30050	−	2.12149i	−0.689399	−	0.157256i
$183$	0.829226			0.0612982
$184$	0.0427395	−	0.0427395i	0.00315080	−	0.00315080i
$185$	−6.32308	+	3.65063i	−0.464882	+	0.268400i
$186$		−	8.14729i		−	0.597388i
$187$	−12.0906	+	45.1227i	−0.884151	+	3.29970i
$188$	0.335258	−	1.25120i	0.0244512	−	0.0912531i
$189$	−2.51346	−	0.826136i	−0.182828	−	0.0600926i
$190$	−8.26176	−	8.26176i	−0.599371	−	0.599371i
$191$	6.31539	−	10.9386i	0.456966	−	0.791488i	−0.541833	−	0.840486i	$-0.682270\pi$
$191$	6.31539	−	10.9386i	0.456966	−	0.791488i	0.998799	+	0.0489981i	$0.0156028\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−0.513811	+	1.91757i	−0.0369850	+	0.138030i	−0.981950	−	0.189143i	$-0.939429\pi$
$193$	−0.513811	+	1.91757i	−0.0369850	+	0.138030i	0.944965	+	0.327172i	$0.106096\pi$
$194$	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	0.924839	−	0.380359i	$-0.124200\pi$
$197$	−0.930208	−	3.47158i	−0.0662746	−	0.247340i	−0.991113	+	0.133019i	$0.957533\pi$
$198$	−6.22339			−0.442277
$199$	10.1883			0.722231			0.361116	−	0.932521i	$-0.382396\pi$
$199$	10.1883			0.722231			0.361116	+	0.932521i	$0.382396\pi$
$200$	0.702801	+	2.62289i	0.0496955	+	0.185466i
$201$	0.840744	−	0.225277i	0.0593015	−	0.0158898i
$202$	−7.78173	−	2.08511i	−0.547521	−	0.146708i
$203$	−5.67415	−	6.34505i	−0.398247	−	0.445335i
$204$	−3.75313	−	6.50061i	−0.262772	−	0.455134i
$205$			6.02152i			0.420561i
$206$	13.3822	+	3.58574i	0.932379	+	0.249830i
$207$	−0.0523450	−	0.0302214i	−0.00363823	−	0.00210053i
$208$	2.30092	−	2.77593i	0.159540	−	0.192476i
$209$			48.1073i			3.32765i
$210$	−2.98093	+	2.66574i	−0.205704	+	0.183953i
$211$	12.7116	−	22.0172i	0.875104	−	1.51573i	0.0184528	−	0.999830i	$-0.494126\pi$
$211$	12.7116	−	22.0172i	0.875104	−	1.51573i	0.856652	−	0.515895i	$-0.172541\pi$
$212$	3.14587	+	1.81627i	0.216059	+	0.124742i
$213$	−0.497499	+	0.133304i	−0.0340881	+	0.00913387i
$214$	7.33177	−	7.33177i	0.501190	−	0.501190i
$215$	1.73777	+	6.48543i	0.118515	+	0.442303i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−1.20135	+	21.5222i	−0.0815531	+	1.46102i
$218$	12.1859	+	7.03553i	0.825333	+	0.476506i
$219$	5.76381	+	5.76381i	0.389482	+	0.389482i
$220$	−4.70328	+	8.14632i	−0.317095	+	0.549225i
$221$	−17.2713	+	20.8368i	−1.16179	+	1.40164i
$222$	−4.18336	+	2.41526i	−0.280769	+	0.162102i
$223$	10.2954	−	2.75865i	0.689432	−	0.184733i	0.102940	−	0.994688i	$-0.467175\pi$
$223$	10.2954	−	2.75865i	0.689432	−	0.184733i	0.586492	+	0.809955i	$0.300508\pi$
$224$	−1.19312	−	2.36145i	−0.0797187	−	0.157781i
$225$	2.35162	−	1.35771i	0.156775	−	0.0905138i
$226$	10.6755	+	2.86049i	0.710123	+	0.190277i
$227$	1.87977	+	1.87977i	0.124765	+	0.124765i	0.766732	−	0.641967i	$-0.221882\pi$
$227$	1.87977	+	1.87977i	0.124765	+	0.124765i	−0.641967	+	0.766732i	$0.721882\pi$
$228$	−5.46599	−	5.46599i	−0.361994	−	0.361994i
$229$	2.42615	+	0.650085i	0.160324	+	0.0429588i	0.338088	−	0.941114i	$-0.390220\pi$
$229$	2.42615	+	0.650085i	0.160324	+	0.0429588i	−0.177764	+	0.984073i	$0.556886\pi$
$230$	−0.0791186	+	0.0456792i	−0.00521693	+	0.00301200i
$231$	16.4400	+	0.917667i	1.08167	+	0.0603780i
$232$	3.10764	−	0.832690i	0.204027	−	0.0546688i
$233$	−17.7000	+	10.2191i	−1.15957	+	0.669475i	−0.951200	−	0.308576i	$-0.900148\pi$
$233$	−17.7000	+	10.2191i	−1.15957	+	0.669475i	−0.208365	+	0.978051i	$0.566814\pi$
$234$	−3.27686	−	1.50405i	−0.214215	−	0.0983230i
$235$	−0.978941	+	1.69558i	−0.0638591	+	0.110607i
$236$	7.03877	+	7.03877i	0.458185	+	0.458185i
$237$	−9.93222	−	5.73437i	−0.645167	−	0.372487i
$238$	8.95587	+	17.7257i	0.580523	+	1.14899i
$239$	−12.0931	+	12.0931i	−0.782235	+	0.782235i	−0.980208	−	0.197972i	$-0.936564\pi$
$239$	−12.0931	+	12.0931i	−0.782235	+	0.782235i	0.197972	+	0.980208i	$0.436564\pi$
$240$	−0.391201	−	1.45998i	−0.0252519	−	0.0942414i
$241$	4.75087	−	4.75087i	0.306030	−	0.306030i	−0.537337	−	0.843367i	$-0.680570\pi$
$241$	4.75087	−	4.75087i	0.306030	−	0.306030i	0.843367	+	0.537337i	$0.180570\pi$
$242$	26.7857	−	7.17721i	1.72185	−	0.461369i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	0.414613	−	0.718131i	0.0265429	−	0.0459736i
$245$	8.26761	−	6.60236i	0.528199	−	0.421810i
$246$			3.98384i			0.254001i
$247$	−11.6264	+	25.3304i	−0.739772	+	1.61173i
$248$	−7.05576	−	4.07364i	−0.448041	−	0.258677i
$249$	−6.48670	−	1.73811i	−0.411078	−	0.110148i
$250$		−	11.6617i		−	0.737553i
$251$	−10.3549	−	17.9352i	−0.653596	−	1.13206i	−0.982244	−	0.187609i	$-0.939926\pi$
$251$	−10.3549	−	17.9352i	−0.653596	−	1.13206i	0.328648	−	0.944453i	$-0.393407\pi$
$252$	−1.97219	+	1.76365i	−0.124236	+	0.111100i
$253$	0.363342	+	0.0973572i	0.0228431	+	0.00612079i
$254$	5.91570	−	1.58511i	0.371184	−	0.0994585i
$255$	2.93646	+	10.9590i	0.183888	+	0.686280i
$256$	1.00000			0.0625000
$257$	−9.50765			−0.593071			−0.296536	−	0.955022i	$-0.595831\pi$
$257$	−9.50765			−0.593071			−0.296536	+	0.955022i	$0.595831\pi$
$258$	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
$262$	−2.98939	+	11.1566i	−0.184685	+	0.689254i
$263$	−8.91400	−	15.4395i	−0.549661	−	0.952041i	−0.998298	−	0.0583263i	$-0.981424\pi$
$263$	−8.91400	−	15.4395i	−0.549661	−	0.952041i	0.448637	−	0.893714i	$-0.351910\pi$
$264$	−3.11170	+	5.38962i	−0.191512	+	0.331708i
$265$	−3.88239	−	3.88239i	−0.238493	−	0.238493i
$266$	13.6332	+	15.2452i	0.835904	+	0.934740i
$267$	−0.742873	+	2.77244i	−0.0454631	+	0.169670i
$268$	0.225277	−	0.840744i	0.0137610	−	0.0513566i
$269$		−	9.15608i		−	0.558256i	−0.960254	−	0.279128i	$-0.909955\pi$
$269$		−	9.15608i		−	0.558256i	0.960254	−	0.279128i	$-0.0900453\pi$
$270$	−1.30898	+	0.755742i	−0.0796622	+	0.0459930i
$271$	−12.0242	+	12.0242i	−0.730418	+	0.730418i	−0.970702	−	0.240285i	$-0.922759\pi$
$271$	−12.0242	+	12.0242i	−0.730418	+	0.730418i	0.240285	+	0.970702i	$0.422759\pi$
$272$	−7.50626			−0.455134
$273$	8.43451	+	4.45635i	0.510480	+	0.269711i
$274$	4.24535			0.256471
$275$	−11.9495	+	11.9495i	−0.720580	+	0.720580i
$276$	−0.0523450	+	0.0302214i	−0.00315080	+	0.00181911i
$277$			11.5333i			0.692968i	0.938056	+	0.346484i	$0.112625\pi$
$277$			11.5333i			0.692968i	−0.938056	+	0.346484i	$0.887375\pi$
$278$	2.25472	−	8.41475i	0.135229	−	0.504683i
$279$	−2.10867	+	7.86967i	−0.126243	+	0.471145i
$280$	0.818131	+	3.91443i	0.0488927	+	0.233932i
$281$	10.6233	+	10.6233i	0.633736	+	0.633736i	0.949003	−	0.315267i	$-0.102094\pi$
$281$	10.6233	+	10.6233i	0.633736	+	0.633736i	−0.315267	+	0.949003i	$0.602094\pi$
$282$	−0.647669	+	1.12180i	−0.0385681	+	0.0668019i
$283$	6.04580	+	10.4716i	0.359386	+	0.622474i	0.987858	−	0.155358i	$-0.0496530\pi$
$283$	6.04580	+	10.4716i	0.359386	+	0.622474i	−0.628473	+	0.777832i	$0.716320\pi$
$284$	−0.133304	+	0.497499i	−0.00791016	+	0.0295211i
$285$	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
$289$	39.3440			2.31435
$290$	−4.86285			−0.285556
$291$	−0.663690	−	2.47693i	−0.0389062	−	0.145200i
$292$	7.87352	−	2.10970i	0.460763	−	0.123461i
$293$	7.51103	+	2.01257i	0.438799	+	0.117576i	0.471454	−	0.881891i	$-0.343729\pi$
$293$	7.51103	+	2.01257i	0.438799	+	0.117576i	−0.0326547	+	0.999467i	$0.510396\pi$
$294$	5.46986	−	4.36813i	0.319009	−	0.254755i
$295$	−7.52290	−	13.0300i	−0.438000	−	0.758639i
$296$			4.83053i			0.280769i
$297$	6.01134	+	1.61073i	0.348813	+	0.0934642i
$298$	4.71289	+	2.72099i	0.273010	+	0.157622i
$299$	0.167785	+	0.139074i	0.00970325	+	0.00804285i
$300$		−	2.71542i		−	0.156775i
$301$	−2.40442	−	11.5042i	−0.138589	−	0.663091i
$302$	−6.85385	+	11.8712i	−0.394395	+	0.683111i
$303$	6.97691	+	4.02812i	0.400813	+	0.231410i
$304$	−7.46668	+	2.00069i	−0.428243	+	0.114747i
$305$	−0.886261	+	0.886261i	−0.0507472	+	0.0507472i
$306$	1.94276	+	7.25049i	0.111060	+	0.414483i
$307$	0.870087	−	0.870087i	0.0496585	−	0.0496585i	−0.681841	−	0.731500i	$-0.738821\pi$
$307$	0.870087	−	0.870087i	0.0496585	−	0.0496585i	0.731500	+	0.681841i	$0.238821\pi$
$308$	9.01470	−	13.7786i	0.513660	−	0.785108i
$309$	−11.9981	−	6.92712i	−0.682549	−	0.394070i
$310$	8.70766	+	8.70766i	0.494562	+	0.494562i
$311$	8.97807	−	15.5505i	0.509100	−	0.881787i	−0.490845	−	0.871247i	$-0.663312\pi$
$311$	8.97807	−	15.5505i	0.509100	−	0.881787i	0.999944	−	0.0105396i	$-0.00335494\pi$
$312$	−2.94098	+	2.08582i	−0.166500	+	0.118086i
$313$	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
$315$	3.56930	−	1.80338i	0.201107	−	0.101609i
$316$	−9.93222	+	5.73437i	−0.558731	+	0.322584i
$317$	0.157858	+	0.0422978i	0.00886617	+	0.00237568i	0.263249	−	0.964728i	$-0.415206\pi$
$317$	0.157858	+	0.0422978i	0.00886617	+	0.00237568i	−0.254383	+	0.967103i	$0.581872\pi$
$318$	−2.56859	−	2.56859i	−0.144040	−	0.144040i
$319$	14.1579	+	14.1579i	0.792691	+	0.792691i
$320$	−1.45998	−	0.391201i	−0.0816155	−	0.0218688i
$321$	−8.97955	+	5.18435i	−0.501190	+	0.289362i
$322$	0.142733	−	0.0721155i	0.00795419	−	0.00401884i
$323$	56.0468	−	15.0177i	3.11853	−	0.835607i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−9.17978	+	3.40395i	−0.509203	+	0.188817i
$326$	−5.90355	+	10.2252i	−0.326967	+	0.566324i
$327$	−9.94974	−	9.94974i	−0.550222	−	0.550222i
$328$	3.45011	+	1.99192i	0.190500	+	0.109985i
$329$	1.87632	−	2.86788i	0.103445	−	0.158111i
$330$	6.65144	−	6.65144i	0.366150	−	0.366150i
$331$	−3.04381	−	11.3596i	−0.167303	−	0.624382i	−0.997735	−	0.0672630i	$-0.978573\pi$
$331$	−3.04381	−	11.3596i	−0.167303	−	0.624382i	0.830433	−	0.557119i	$-0.188093\pi$
$332$	−4.74859	+	4.74859i	−0.260613	+	0.260613i
$333$	4.66593	−	1.25023i	0.255691	−	0.0685123i
$334$	7.73378	+	4.46510i	0.423174	+	0.244320i
$335$	−0.657800	+	1.13934i	−0.0359394	+	0.0622489i
$336$	0.541277	+	2.58979i	0.0295291	+	0.141285i
$337$			18.5295i			1.00937i	0.863304	+	0.504684i	$0.168391\pi$
$337$			18.5295i			1.00937i	−0.863304	+	0.504684i	$0.831609\pi$
$338$	10.7381	+	7.32761i	0.584074	+	0.398569i
$339$	−9.57138	−	5.52604i	−0.519846	−	0.300133i
$340$	10.9590	+	2.93646i	0.594335	+	0.159252i
$341$		−	50.7038i		−	2.74576i
$342$	3.86504	+	6.69444i	0.208997	+	0.361994i
$343$	−15.0935	+	10.7325i	−0.814973	+	0.579499i
$344$	4.29077	+	1.14971i	0.231343	+	0.0619881i
$345$	0.0882454	−	0.0236453i	0.00475097	−	0.00127302i
$346$	−5.73636	−	21.4084i	−0.308389	−	1.15092i
$347$	−29.8885			−1.60450			−0.802250	−	0.596989i	$-0.796364\pi$
$347$	−29.8885			−1.60450			−0.802250	+	0.596989i	$0.796364\pi$
$348$	−3.21727			−0.172464
$349$	2.72772	+	10.1800i	0.146012	+	0.544923i	0.999708	+	0.0241523i	$0.00768866\pi$
$349$	2.72772	+	10.1800i	0.146012	+	0.544923i	−0.853697	+	0.520771i	$0.825645\pi$
$350$	−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
$353$	−9.20112	+	34.3391i	−0.489726	+	1.82768i	0.0680359	+	0.997683i	$0.478327\pi$
$353$	−9.20112	+	34.3391i	−0.489726	+	1.82768i	−0.557762	+	0.830001i	$0.688340\pi$
$354$	−4.97716	−	8.62070i	−0.264533	−	0.458185i
$355$	0.389244	−	0.674191i	0.0206589	−	0.0357823i
$356$	2.02957	+	2.02957i	0.107567	+	0.107567i
$357$	−4.06296	−	19.4397i	−0.215035	−	1.02886i
$358$	−2.54535	+	9.49938i	−0.134526	+	0.502058i
$359$	−0.397498	+	1.48348i	−0.0209791	+	0.0782952i	−0.975622	−	0.219459i	$-0.929571\pi$
$359$	−0.397498	+	1.48348i	−0.0209791	+	0.0782952i	0.954643	+	0.297754i	$0.0962375\pi$
$360$			1.51148i			0.0796622i
$361$	35.2940	−	20.3770i	1.85758	−	1.07247i
$362$	8.00233	−	8.00233i	0.420593	−	0.420593i
$363$	−27.7306			−1.45548
$364$	8.07657	−	5.07632i	0.423327	−	0.266072i
$365$	−12.3205			−0.644885
$366$	−0.586351	+	0.586351i	−0.0306491	+	0.0306491i
$367$	−4.77439	+	2.75649i	−0.249221	+	0.143888i	−0.619408	−	0.785070i	$-0.712627\pi$
$367$	−4.77439	+	2.75649i	−0.249221	+	0.143888i	0.370186	+	0.928957i	$0.379294\pi$
$368$			0.0604428i			0.00315080i
$369$	1.03109	−	3.84810i	0.0536766	−	0.200324i
$370$	1.88971	−	7.05248i	0.0982412	−	0.366641i
$371$	6.40655	+	7.16405i	0.332611	+	0.371939i
$372$	5.76100	+	5.76100i	0.298694	+	0.298694i
$373$	9.47273	−	16.4073i	0.490480	−	0.849535i	−0.509460	−	0.860494i	$-0.670155\pi$
$373$	9.47273	−	16.4073i	0.490480	−	0.849535i	0.999940	+	0.0109586i	$0.00348830\pi$
$374$	−23.3572	−	40.4559i	−1.20777	−	2.09192i
$375$	−3.01828	+	11.2644i	−0.155863	+	0.581689i
$376$	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	−0.672892	−	0.739740i	$-0.734948\pi$
$379$	−8.95565	−	33.4229i	−0.460021	−	1.71682i	0.212872	−	0.977080i	$-0.431718\pi$
$380$	11.6839			0.599371
$381$	−6.12439			−0.313762
$382$	3.26909	+	12.2004i	0.167261	+	0.624227i
$383$	−22.4731	+	6.02166i	−1.14832	+	0.307692i	−0.782293	−	0.622910i	$-0.785950\pi$
$383$	−22.4731	+	6.02166i	−1.14832	+	0.307692i	−0.366031	+	0.930603i	$0.619283\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	−18.5515	+	16.5899i	−0.945472	+	0.845501i
$386$	−0.992608	−	1.71925i	−0.0505224	−	0.0875073i
$387$		−	4.44213i		−	0.225806i
$388$	−2.47693	−	0.663690i	−0.125747	−	0.0336938i
$389$	17.4192	+	10.0570i	0.883190	+	0.509910i	0.871709	−	0.490024i	$-0.163012\pi$
$389$	17.4192	+	10.0570i	0.883190	+	0.509910i	0.0114814	+	0.999934i	$0.496345\pi$
$390$	5.10975	−	1.89475i	0.258742	−	0.0959442i
$391$		−	0.453699i		−	0.0229446i
$392$	−1.04798	−	6.92111i	−0.0529310	−	0.349569i
$393$	5.77506	−	10.0027i	0.291313	−	0.504569i
$394$	3.11254	+	1.79702i	0.156807	+	0.0905327i
$395$	16.7442	−	4.48658i	0.842490	−	0.225745i
$396$	4.40060	−	4.40060i	0.221139	−	0.221139i
$397$	3.91863	+	14.6245i	0.196670	+	0.733983i	0.991828	+	0.127581i	$0.0407212\pi$
$397$	3.91863	+	14.6245i	0.196670	+	0.733983i	−0.795158	+	0.606402i	$0.792612\pi$
$398$	−7.20424	+	7.20424i	−0.361116	+	0.361116i
$399$	−9.22291	−	18.2542i	−0.461723	−	0.913854i
$400$	−2.35162	−	1.35771i	−0.117581	−	0.0678854i
$401$	−13.3944	−	13.3944i	−0.668886	−	0.668886i	0.288572	−	0.957458i	$-0.406820\pi$
$401$	−13.3944	−	13.3944i	−0.668886	−	0.668886i	−0.957458	+	0.288572i	$0.906820\pi$
$402$	−0.435201	+	0.753791i	−0.0217059	+	0.0375957i
$403$	12.2539	−	26.6975i	0.610412	−	1.32990i
$404$	6.97691	−	4.02812i	0.347114	−	0.200407i
$405$	1.45998	−	0.391201i	0.0725471	−	0.0194389i
$406$	8.49886	+	0.474400i	0.421791	+	0.0235441i
$407$	−26.0347	+	15.0311i	−1.29049	+	0.745066i
$408$	7.25049	+	1.94276i	0.358953	+	0.0961811i
$409$	19.2319	+	19.2319i	0.950956	+	0.950956i	0.998852	−	0.0478963i	$-0.0152517\pi$
$409$	19.2319	+	19.2319i	0.950956	+	0.950956i	−0.0478963	+	0.998852i	$0.515252\pi$
$410$	−4.25785	−	4.25785i	−0.210280	−	0.210280i
$411$	−4.10069	−	1.09878i	−0.202272	−	0.0541987i
$412$	−11.9981	+	6.92712i	−0.591105	+	0.341275i
$413$	11.8767	+	23.5067i	0.584414	+	1.15669i
$414$	0.0583833	−	0.0156437i	0.00286938	−	0.000768848i
$415$	8.79051	−	5.07521i	0.431509	−	0.249132i
$416$	0.335884	+	3.58987i	0.0164680	+	0.176008i
$417$	−4.35579	+	7.54445i	−0.213304	+	0.369454i
$418$	−34.0170	−	34.0170i	−1.66383	−	1.66383i
$419$	6.33740	+	3.65890i	0.309602	+	0.178749i	0.646748	−	0.762703i	$-0.276128\pi$
$419$	6.33740	+	3.65890i	0.309602	+	0.178749i	−0.337146	+	0.941452i	$0.609462\pi$
$420$	0.222875	−	3.99280i	0.0108752	−	0.194829i
$421$	−14.2023	+	14.2023i	−0.692178	+	0.692178i	−0.962711	−	0.270532i	$-0.912800\pi$
$421$	−14.2023	+	14.2023i	−0.692178	+	0.692178i	0.270532	+	0.962711i	$0.412800\pi$
$422$	6.58002	+	24.5570i	0.320310	+	1.19541i
$423$	0.915942	−	0.915942i	0.0445346	−	0.0445346i
$424$	−3.50876	+	0.940170i	−0.170401	+	0.0456587i
$425$	17.6519	+	10.1913i	0.856241	+	0.494351i
$426$	0.257524	−	0.446045i	0.0124771	−	0.0216110i
$427$	1.63539	−	1.46247i	0.0791420	−	0.0707738i
$428$			10.3687i			0.501190i
$429$	−20.3932	−	9.36031i	−0.984593	−	0.451920i
$430$	−5.81468	−	3.35711i	−0.280409	−	0.161894i
$431$	−3.03918	−	0.814347i	−0.146392	−	0.0392257i	0.184879	−	0.982761i	$-0.440811\pi$
$431$	−3.03918	−	0.814347i	−0.146392	−	0.0392257i	−0.331271	+	0.943536i	$0.607477\pi$
$432$			1.00000i			0.0481125i
$433$	0.586750	+	1.01628i	0.0281974	+	0.0488394i	0.879780	−	0.475381i	$-0.157690\pi$
$433$	0.586750	+	1.01628i	0.0281974	+	0.0488394i	−0.851582	+	0.524221i	$0.824357\pi$
$434$	−14.3690	−	16.0680i	−0.689734	−	0.771287i
$435$	4.69715	+	1.25860i	0.225211	+	0.0603451i
$436$	−13.5916	+	3.64186i	−0.650919	+	0.174413i
$437$	−0.120927	−	0.451307i	−0.00578474	−	0.0215889i
$438$	−8.15126			−0.389482
$439$	−28.0053			−1.33662			−0.668310	−	0.743883i	$-0.732982\pi$
$439$	−28.0053			−1.33662			−0.668310	+	0.743883i	$0.732982\pi$
$440$	−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	$0.945704\pi$
$444$	1.25023	−	4.66593i	0.0593334	−	0.221435i
$445$	−2.16916	−	3.75710i	−0.102828	−	0.178103i
$446$	−5.32930	+	9.23062i	−0.252350	+	0.437082i
$447$	−3.84805	−	3.84805i	−0.182007	−	0.182007i
$448$	2.51346	+	0.826136i	0.118750	+	0.0390313i
$449$	8.54677	−	31.8970i	0.403347	−	1.50531i	−0.403737	−	0.914875i	$-0.632289\pi$
$449$	8.54677	−	31.8970i	0.403347	−	1.50531i	0.807084	−	0.590437i	$-0.201044\pi$
$450$	−0.702801	+	2.62289i	−0.0331304	+	0.123644i
$451$			24.7930i			1.16746i
$452$	−9.57138	+	5.52604i	−0.450200	+	0.259923i
$453$	9.69280	−	9.69280i	0.455408	−	0.455408i
$454$	−2.65839			−0.124765
$455$	−13.7775	+	4.25178i	−0.645899	+	0.199326i
$456$	7.73007			0.361994
$457$	16.6020	−	16.6020i	0.776610	−	0.776610i	−0.202643	−	0.979253i	$-0.564953\pi$
$457$	16.6020	−	16.6020i	0.776610	−	0.776610i	0.979253	+	0.202643i	$0.0649531\pi$
$458$	−2.17523	+	1.25587i	−0.101642	+	0.0586828i
$459$		−	7.50626i		−	0.350362i
$460$	0.0236453	−	0.0882454i	0.00110247	−	0.00411446i
$461$	7.65826	−	28.5810i	0.356681	−	1.33115i	−0.521675	−	0.853144i	$-0.674693\pi$
$461$	7.65826	−	28.5810i	0.356681	−	1.33115i	0.878356	−	0.478007i	$-0.158641\pi$
$462$	−12.2737	+	10.9759i	−0.571024	+	0.510646i
$463$	−15.1405	−	15.1405i	−0.703641	−	0.703641i	0.261549	−	0.965190i	$-0.415767\pi$
$463$	−15.1405	−	15.1405i	−0.703641	−	0.703641i	−0.965190	+	0.261549i	$0.915767\pi$
$464$	−1.60863	+	2.78623i	−0.0746789	+	0.129348i
$465$	−6.15725	−	10.6647i	−0.285536	−	0.494562i
$466$	5.28979	−	19.7418i	0.245045	−	0.914520i
$467$	14.4895	+	25.0965i	0.670493	+	1.16133i	0.977765	+	0.209706i	$0.0672506\pi$
$467$	14.4895	+	25.0965i	0.670493	+	1.16133i	−0.307272	+	0.951622i	$0.599416\pi$
$468$	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
$471$	22.3191			1.02841
$472$	−9.95432			−0.458185
$473$	7.15509	+	26.7032i	0.328991	+	1.22781i
$474$	11.0780	−	2.96833i	0.508827	−	0.136340i
$475$	20.2751	+	5.43270i	0.930287	+	0.249270i
$476$	−18.8667	−	6.20120i	−0.864754	−	0.284231i
$477$	1.81627	+	3.14587i	0.0831613	+	0.144040i
$478$		−	17.1022i		−	0.782235i
$479$	−28.3587	−	7.59870i	−1.29574	−	0.347193i	−0.455904	−	0.890029i	$-0.650684\pi$
$479$	−28.3587	−	7.59870i	−1.29574	−	0.347193i	−0.839839	+	0.542835i	$0.817351\pi$
$480$	1.30898	+	0.755742i	0.0597467	+	0.0344948i
$481$	−17.3410	+	1.62249i	−0.790680	+	0.0739794i
$482$			6.71874i			0.306030i
$483$	−0.156534	+	0.0327163i	−0.00712255	+	0.00148864i
$484$	−13.8653	+	24.0154i	−0.630242	+	1.09161i
$485$	3.35663	+	1.93795i	0.152417	+	0.0879979i
$486$	0.965926	−	0.258819i	0.0438153	−	0.0117403i
$487$	20.3250	−	20.3250i	0.921013	−	0.921013i	−0.0760879	−	0.997101i	$-0.524243\pi$
$487$	20.3250	−	20.3250i	0.921013	−	0.921013i	0.997101	+	0.0760879i	$0.0242430\pi$
$488$	0.214619	+	0.800971i	0.00971537	+	0.0362582i
$489$	8.34888	−	8.34888i	0.377549	−	0.377549i
$490$	−1.17751	+	10.5147i	−0.0531945	+	0.475004i
$491$	27.7851	+	16.0417i	1.25392	+	0.723953i	0.971887	−	0.235450i	$-0.0756563\pi$
$491$	27.7851	+	16.0417i	1.25392	+	0.723953i	0.282038	+	0.959403i	$0.408990\pi$
$492$	−2.81700	−	2.81700i	−0.127000	−	0.127000i
$493$	12.0748	−	20.9142i	0.543823	−	0.941928i
$494$	−9.69016	−	26.1324i	−0.435981	−	1.17575i
$495$	−8.14632	+	4.70328i	−0.366150	+	0.211397i
$496$	7.86967	−	2.10867i	0.353359	−	0.0946822i
$497$	−0.746058	+	1.14032i	−0.0334653	+	0.0511503i
$498$	5.81582	−	3.35776i	0.260613	−	0.150465i
$499$	−3.21674	−	0.861922i	−0.144001	−	0.0385849i	0.186099	−	0.982531i	$-0.440416\pi$
$499$	−3.21674	−	0.861922i	−0.144001	−	0.0385849i	−0.330099	+	0.943946i	$0.607082\pi$
$500$	8.24609	+	8.24609i	0.368776	+	0.368776i
$501$	−6.31461	−	6.31461i	−0.282116	−	0.282116i
$502$	20.0042	+	5.36010i	0.892829	+	0.239233i
$503$	35.7390	−	20.6339i	1.59352	−	0.920020i	0.600825	−	0.799380i	$-0.294839\pi$
$503$	35.7390	−	20.6339i	1.59352	−	0.920020i	0.992696	−	0.120640i	$-0.0384945\pi$
$504$	0.147454	−	2.64164i	0.00656814	−	0.117668i
$505$	−11.7620	+	3.15161i	−0.523401	+	0.140245i
$506$	−0.325764	+	0.188080i	−0.0144820	+	0.00836116i
$507$	−8.47565	−	9.85715i	−0.376417	−	0.437771i
$508$	−3.06219	+	5.30387i	−0.135863	+	0.235321i
$509$	−18.2731	−	18.2731i	−0.809939	−	0.809939i	0.174685	−	0.984624i	$-0.444109\pi$
$509$	−18.2731	−	18.2731i	−0.809939	−	0.809939i	−0.984624	+	0.174685i	$0.944109\pi$
$510$	−9.82558	−	5.67280i	−0.435084	−	0.251196i
$511$	21.5327	+	1.20194i	0.952551	+	0.0531707i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.00069	−	7.46668i	−0.0883326	−	0.329662i
$514$	6.72293	−	6.72293i	0.296536	−	0.296536i
$515$	20.2269	−	5.41979i	0.891305	−	0.238824i
$516$	−3.84700	−	2.22107i	−0.169355	−	0.0977770i
$517$	−4.03070	+	6.98137i	−0.177270	+	0.307040i
$518$	−3.99068	+	12.1414i	−0.175340	+	0.533460i
$519$			22.1636i			0.972873i
$520$	0.913978	−	5.37255i	0.0400806	−	0.235602i
$521$	−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	$0.737006\pi$
$522$	3.10764	+	0.832690i	0.136018	+	0.0364458i
$523$			39.9433i			1.74660i	0.487184	+	0.873299i	$0.338024\pi$
$523$			39.9433i			1.74660i	−0.487184	+	0.873299i	$0.661976\pi$
$524$	−5.77506	−	10.0027i	−0.252284	−	0.436970i
$525$	2.24330	−	6.82510i	0.0979058	−	0.297872i
$526$	17.2205	+	4.61423i	0.750851	+	0.201190i
$527$	−59.0718	+	15.8282i	−2.57321	+	0.689489i
$528$	−1.61073	−	6.01134i	−0.0700981	−	0.261610i
$529$	22.9963			0.999841
$530$	5.49053			0.238493
$531$	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
$535$	4.05624	−	15.1381i	0.175367	−	0.654477i
$536$	0.435201	+	0.753791i	0.0187978	+	0.0325588i
$537$	4.91724	−	8.51691i	0.212195	−	0.367532i
$538$	6.47432	+	6.47432i	0.279128	+	0.279128i
$539$	34.0411	−	27.1846i	1.46625	−	1.17092i
$540$	0.391201	−	1.45998i	0.0168346	−	0.0628276i
$541$	5.85623	−	21.8557i	0.251779	−	0.939652i	−0.718075	−	0.695966i	$-0.754977\pi$
$541$	5.85623	−	21.8557i	0.251779	−	0.939652i	0.969854	−	0.243686i	$-0.0783567\pi$
$542$		−	17.0048i		−	0.730418i
$543$	−9.80082	+	5.65850i	−0.420593	+	0.242830i
$544$	5.30773	−	5.30773i	0.227567	−	0.227567i
$545$	21.2682			0.911029
$546$	−9.11521	+	2.81298i	−0.390095	+	0.120385i
$547$	35.2646			1.50781			0.753904	−	0.656985i	$-0.228168\pi$
$547$	35.2646			1.50781			0.753904	+	0.656985i	$0.228168\pi$
$548$	−3.00191	+	3.00191i	−0.128235	+	0.128235i
$549$	0.718131	−	0.414613i	0.0306491	−	0.0176953i
$550$		−	16.8991i		−	0.720580i
$551$	6.43675	−	24.0223i	0.274215	−	1.02338i
$552$	0.0156437	−	0.0583833i	0.000665842	−	0.00248496i
$553$	−29.7017	+	6.20776i	−1.26304	+	0.263981i
$554$	−8.15527	−	8.15527i	−0.346484	−	0.346484i
$555$	−3.65063	+	6.32308i	−0.154961	+	0.268400i
$556$	4.35579	+	7.54445i	0.184727	+	0.319956i
$557$	2.86542	−	10.6939i	0.121412	−	0.453116i	−0.878274	−	0.478157i	$-0.841305\pi$
$557$	2.86542	−	10.6939i	0.121412	−	0.453116i	0.999686	+	0.0250413i	$0.00797172\pi$
$558$	−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
$562$	−15.0237			−0.633736
$563$	−15.8046			−0.666086			−0.333043	−	0.942912i	$-0.608075\pi$
$563$	−15.8046			−0.666086			−0.333043	+	0.942912i	$0.608075\pi$
$564$	−0.335258	−	1.25120i	−0.0141169	−	0.0526850i
$565$	16.1358	−	4.32358i	0.678840	−	0.181895i
$566$	−11.6796	−	3.12954i	−0.490930	−	0.131544i
$567$	−2.58979	+	0.541277i	−0.108761	+	0.0227315i
$568$	−0.257524	−	0.446045i	−0.0108055	−	0.0187157i
$569$			39.6028i			1.66024i	0.557587	+	0.830118i	$0.311727\pi$
$569$			39.6028i			1.66024i	−0.557587	+	0.830118i	$0.688273\pi$
$570$	−11.2858	−	3.02401i	−0.472709	−	0.126662i
$571$	−9.31305	−	5.37689i	−0.389739	−	0.225016i	0.292308	−	0.956324i	$-0.405577\pi$
$571$	−9.31305	−	5.37689i	−0.389739	−	0.225016i	−0.682047	+	0.731308i	$0.738910\pi$
$572$	−18.3029	+	12.9809i	−0.765281	+	0.542758i
$573$		−	12.6308i		−	0.527659i
$574$	7.02612	+	7.85688i	0.293265	+	0.327940i
$575$	0.0820636	−	0.142138i	0.00342229	−	0.00592758i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	−19.2078	+	5.14672i	−0.799633	+	0.214261i	−0.635423	−	0.772165i	$-0.719174\pi$
$577$	−19.2078	+	5.14672i	−0.799633	+	0.214261i	−0.164210	+	0.986425i	$0.552507\pi$
$578$	−27.8204	+	27.8204i	−1.15718	+	1.15718i
$579$	0.513811	+	1.91757i	0.0213533	+	0.0796915i
$580$	3.43855	−	3.43855i	0.142778	−	0.142778i
$581$	−15.8584	+	8.01243i	−0.657917	+	0.332412i
$582$	2.22075	+	1.28215i	0.0920531	+	0.0531469i
$583$	−15.9854	−	15.9854i	−0.662046	−	0.662046i
$584$	−4.07563	+	7.05920i	−0.168651	+	0.292112i
$585$	−5.42604	+	0.507683i	−0.224339	+	0.0209901i
$586$	−6.73420	+	3.88799i	−0.278187	+	0.160612i
$587$	−14.9755	+	4.01267i	−0.618104	+	0.165621i	−0.554266	−	0.832340i	$-0.687001\pi$
$587$	−14.9755	+	4.01267i	−0.618104	+	0.165621i	−0.0638384	+	0.997960i	$0.520334\pi$
$588$	−0.779042	+	6.95651i	−0.0321272	+	0.286882i
$589$	−54.5415	+	31.4896i	−2.24734	+	1.29750i
$590$	14.5331	+	3.89414i	0.598319	+	0.160319i
$591$	−2.54137	−	2.54137i	−0.104538	−	0.104538i
$592$	−3.41570	−	3.41570i	−0.140384	−	0.140384i
$593$	42.0426	+	11.2653i	1.72648	+	0.462609i	0.979368	−	0.202086i	$-0.0647721\pi$
$593$	42.0426	+	11.2653i	1.72648	+	0.462609i	0.747114	+	0.664696i	$0.231439\pi$
$594$	−5.38962	+	3.11170i	−0.221139	+	0.127674i
$595$	25.1191	+	16.4343i	1.02978	+	0.673741i
$596$	−5.25654	+	1.40849i	−0.215316	+	0.0576938i
$597$	8.82335	−	5.09416i	0.361116	−	0.208490i
$598$	−0.216982	+	0.0203017i	−0.00887305	+	0.000830200i
$599$	−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	$0.243511\pi$
$600$	1.92009	+	1.92009i	0.0783873	+	0.0783873i
$601$	−13.8487	−	7.99556i	−0.564901	−	0.326146i	0.190209	−	0.981744i	$-0.439083\pi$
$601$	−13.8487	−	7.99556i	−0.564901	−	0.326146i	−0.755110	+	0.655598i	$0.772417\pi$
$602$	9.83488	+	6.43451i	0.400840	+	0.262251i
$603$	0.615467	−	0.615467i	0.0250638	−	0.0250638i
$604$	−3.54781	−	13.2406i	−0.144358	−	0.538753i
$605$	29.6380	−	29.6380i	1.20495	−	1.20495i
$606$	−7.78173	+	2.08511i	−0.316111	+	0.0847018i
$607$	−5.52809	−	3.19165i	−0.224378	−	0.129545i	0.383598	−	0.923500i	$-0.374685\pi$
$607$	−5.52809	−	3.19165i	−0.224378	−	0.129545i	−0.607976	+	0.793955i	$0.708018\pi$
$608$	3.86504	−	6.69444i	0.156748	−	0.271495i
$609$	−8.08648	−	2.65790i	−0.327681	−	0.107704i
$610$		−	1.25336i		−	0.0507472i
$611$	−3.80956	+	2.70184i	−0.154118	+	0.109305i
$612$	−6.50061	−	3.75313i	−0.262772	−	0.151711i
$613$	−45.4091	−	12.1673i	−1.83406	−	0.491434i	−0.835723	−	0.549151i	$-0.814951\pi$
$613$	−45.4091	−	12.1673i	−1.83406	−	0.491434i	−0.998333	+	0.0577177i	$0.981618\pi$
$614$			1.23049i			0.0496585i
$615$	3.01076	+	5.21479i	0.121405	+	0.210280i
$616$	3.36858	+	16.1173i	0.135724	+	0.649384i
$617$	−16.0799	−	4.30860i	−0.647354	−	0.173458i	−0.0798215	−	0.996809i	$-0.525435\pi$
$617$	−16.0799	−	4.30860i	−0.647354	−	0.173458i	−0.567532	+	0.823351i	$0.692102\pi$
$618$	13.3822	−	3.58574i	0.538310	−	0.144240i
$619$	7.34176	+	27.3998i	0.295090	+	1.10129i	0.941146	+	0.338001i	$0.109751\pi$
$619$	7.34176	+	27.3998i	0.295090	+	1.10129i	−0.646055	+	0.763290i	$0.723583\pi$
$620$	−12.3145			−0.494562
$621$	−0.0604428			−0.00242549
$622$	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
$626$	−0.120448	+	0.449518i	−0.00481407	+	0.0179663i
$627$	24.0536	+	41.6621i	0.960610	+	1.66383i
$628$	11.1595	−	19.3289i	0.445314	−	0.771306i
$629$	25.6391	+	25.6391i	1.02230	+	1.02230i
$630$	−1.24869	+	3.79906i	−0.0497491	+	0.151358i
$631$	−6.29363	+	23.4882i	−0.250546	+	0.935049i	0.719969	+	0.694006i	$0.244156\pi$
$631$	−6.29363	+	23.4882i	−0.250546	+	0.935049i	−0.970515	+	0.241043i	$0.922511\pi$
$632$	2.96833	−	11.0780i	0.118074	−	0.440657i
$633$		−	25.4233i		−	1.01048i
$634$	−0.141531	+	0.0817132i	−0.00562093	+	0.00324524i
$635$	6.54563	−	6.54563i	0.259755	−	0.259755i
$636$	3.63254			0.144040
$637$	24.4939	−	6.08680i	0.970483	−	0.241168i
$638$	−20.0223			−0.792691
$639$	−0.364195	+	0.364195i	−0.0144073	+	0.0144073i
$640$	1.30898	−	0.755742i	0.0517421	−	0.0298733i
$641$		−	27.8258i		−	1.09905i	−0.835476	−	0.549527i	$-0.814808\pi$
$641$		−	27.8258i		−	1.09905i	0.835476	−	0.549527i	$-0.185192\pi$
$642$	2.68362	−	10.0154i	0.105914	−	0.395276i
$643$	5.95094	−	22.2092i	0.234682	−	0.875846i	−0.743610	−	0.668614i	$-0.766888\pi$
$643$	5.95094	−	22.2092i	0.234682	−	0.875846i	0.978292	−	0.207232i	$-0.0664454\pi$
$644$	−0.0499340	+	0.151921i	−0.00196768	+	0.00598652i
$645$	4.74767	+	4.74767i	0.186939	+	0.186939i
$646$	−29.0120	+	50.2502i	−1.14146	+	1.97707i
$647$	5.78195	+	10.0146i	0.227312	+	0.393715i	0.957010	−	0.290053i	$-0.0936730\pi$
$647$	5.78195	+	10.0146i	0.227312	+	0.393715i	−0.729699	+	0.683769i	$0.760340\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	−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
$653$	8.23574			0.322289			0.161145	−	0.986931i	$-0.448481\pi$
$653$	8.23574			0.322289			0.161145	+	0.986931i	$0.448481\pi$
$654$	14.0711			0.550222
$655$	4.51841	+	16.8630i	0.176549	+	0.658890i
$656$	−3.84810	+	1.03109i	−0.150243	+	0.0402575i
$657$	7.87352	+	2.10970i	0.307175	+	0.0823073i
$658$	0.701136	+	3.35465i	0.0273331	+	0.130778i
$659$	−12.9134	−	22.3667i	−0.503036	−	0.871283i	−0.999994	−	0.00350872i	$-0.998883\pi$
$659$	−12.9134	−	22.3667i	−0.503036	−	0.871283i	0.496958	−	0.867774i	$-0.334450\pi$
$660$			9.40656i			0.366150i
$661$	−26.4617	−	7.09039i	−1.02924	−	0.275784i	−0.295593	−	0.955314i	$-0.595517\pi$
$661$	−26.4617	−	7.09039i	−1.02924	−	0.275784i	−0.733648	+	0.679530i	$0.762184\pi$
$662$	10.1848	+	5.88018i	0.395842	+	0.228540i
$663$	−4.53895	+	26.6809i	−0.176278	+	1.03620i
$664$		−	6.71552i		−	0.260613i
$665$	29.3670	+	9.65249i	1.13880	+	0.374307i
$666$	−2.41526	+	4.18336i	−0.0935896	+	0.162102i
$667$	−0.168408	−	0.0972303i	−0.00652078	−	0.00376477i
$668$	−8.62592	+	2.31131i	−0.333747	+	0.0894272i
$669$	7.53677	−	7.53677i	0.291388	−	0.291388i
$670$	−0.340502	−	1.27077i	−0.0131547	−	0.0490942i
$671$	−3.64910	+	3.64910i	−0.140872	+	0.140872i
$672$	−2.21400	−	1.44852i	−0.0854069	−	0.0558778i
$673$	−19.5143	−	11.2666i	−0.752220	−	0.434294i	0.0742756	−	0.997238i	$-0.476336\pi$
$673$	−19.5143	−	11.2666i	−0.752220	−	0.434294i	−0.826495	+	0.562943i	$0.809669\pi$
$674$	−13.1024	−	13.1024i	−0.504684	−	0.504684i
$675$	1.35771	−	2.35162i	0.0522582	−	0.0905138i
$676$	−12.7744	+	2.41156i	−0.491322	+	0.0927522i
$677$	−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
$679$	−5.67737	−	3.71444i	−0.217877	−	0.142547i
$680$	−9.82558	+	5.67280i	−0.376794	+	0.217542i
$681$	2.56781	+	0.688042i	0.0983987	+	0.0263658i
$682$	35.8530	+	35.8530i	1.37288	+	1.37288i
$683$	2.30907	+	2.30907i	0.0883542	+	0.0883542i	0.749903	−	0.661548i	$-0.230100\pi$
$683$	2.30907	+	2.30907i	0.0883542	+	0.0883542i	−0.661548	+	0.749903i	$0.730100\pi$
$684$	−7.46668	−	2.00069i	−0.285496	−	0.0764983i
$685$	5.55709	−	3.20839i	0.212326	−	0.122586i
$686$	3.08372	−	18.2617i	0.117737	−	0.697236i
$687$	2.42615	−	0.650085i	0.0925633	−	0.0248023i
$688$	−3.84700	+	2.22107i	−0.146666	+	0.0846774i
$689$	−4.55363	−	12.2802i	−0.173479	−	0.467839i
$690$	−0.0456792	+	0.0791186i	−0.00173898	+	0.00301200i
$691$	−11.9062	−	11.9062i	−0.452933	−	0.452933i	0.443394	−	0.896327i	$-0.353774\pi$
$691$	−11.9062	−	11.9062i	−0.452933	−	0.452933i	−0.896327	+	0.443394i	$0.853774\pi$
$692$	19.1942	+	11.0818i	0.729655	+	0.421267i
$693$	14.6963	−	7.42526i	0.558265	−	0.282062i
$694$	21.1344	−	21.1344i	0.802250	−	0.802250i
$695$	−3.40798	−	12.7188i	−0.129272	−	0.482450i
$696$	2.27495	−	2.27495i	0.0862318	−	0.0862318i
$697$	28.8848	−	7.73966i	1.09409	−	0.293161i
$698$	−9.12714	−	5.26956i	−0.345467	−	0.199456i
$699$	−10.2191	+	17.7000i	−0.386522	+	0.669475i
$700$	−4.78906	−	5.35531i	−0.181009	−	0.202412i
$701$		−	7.65213i		−	0.289017i	−0.989504	−	0.144509i	$-0.953840\pi$
$701$		−	7.65213i		−	0.289017i	0.989504	−	0.144509i	$-0.0461601\pi$
$702$	−3.58987	+	0.335884i	−0.135491	+	0.0126771i
$703$	32.3377	+	18.6702i	1.21964	+	0.704159i
$704$	−6.01134	−	1.61073i	−0.226561	−	0.0607068i
$705$			1.95788i			0.0737381i
$706$	−17.7752	−	30.7876i	−0.668979	−	1.15871i
$707$	20.8640	−	4.36066i	0.784671	−	0.163999i
$708$	9.61514	+	2.57637i	0.361359	+	0.0968258i
$709$	−4.88615	+	1.30924i	−0.183503	+	0.0491695i	−0.349400	−	0.936974i	$-0.613615\pi$
$709$	−4.88615	+	1.30924i	−0.183503	+	0.0491695i	0.165897	+	0.986143i	$0.446948\pi$
$710$	0.201488	+	0.751962i	0.00756170	+	0.0282206i
$711$	−11.4687			−0.430112
$712$	−2.87024			−0.107567
$713$	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
$717$	−4.42637	+	16.5194i	−0.165306	+	0.616929i
$718$	−0.767907	−	1.33005i	−0.0286580	−	0.0496372i
$719$	14.2681	−	24.7131i	0.532110	−	0.921642i	−0.467187	−	0.884159i	$-0.654732\pi$
$719$	14.2681	−	24.7131i	0.532110	−	0.921642i	0.999297	−	0.0374835i	$-0.0119342\pi$
$720$	−1.06878	−	1.06878i	−0.0398311	−	0.0398311i
$721$	−35.8796	+	7.49897i	−1.33623	+	0.279276i
$722$	−10.5479	+	39.3654i	−0.392553	+	1.46503i
$723$	1.73894	−	6.48980i	0.0646718	−	0.241358i
$724$			11.3170i			0.420593i
$725$	7.56578	−	4.36811i	0.280986	−	0.162227i
$726$	19.6085	−	19.6085i	0.727740	−	0.727740i
$727$	23.9463			0.888119			0.444060	−	0.895997i	$-0.353538\pi$
$727$	23.9463			0.888119			0.444060	+	0.895997i	$0.353538\pi$
$728$	−2.12149	+	9.30050i	−0.0786278	+	0.344699i
$729$	−1.00000			−0.0370370
$730$	8.71192	−	8.71192i	0.322442	−	0.322442i
$731$	28.8766	−	16.6719i	1.06804	−	0.616633i
$732$		−	0.829226i		−	0.0306491i
$733$	12.0230	−	44.8705i	0.444080	−	1.65733i	−0.274274	−	0.961652i	$-0.588437\pi$
$733$	12.0230	−	44.8705i	0.444080	−	1.65733i	0.718354	−	0.695678i	$-0.244896\pi$
$734$	1.42687	−	5.32514i	0.0526666	−	0.196554i
$735$	3.85878	−	9.85162i	0.142333	−	0.363383i
$736$	−0.0427395	−	0.0427395i	−0.00157540	−	0.00157540i
$737$	−2.70843	+	4.69114i	−0.0997662	+	0.172800i
$738$	1.99192	+	3.45011i	0.0733236	+	0.127000i
$739$	−4.86694	+	18.1637i	−0.179033	+	0.668162i	0.816796	+	0.576927i	$0.195748\pi$
$739$	−4.86694	+	18.1637i	−0.179033	+	0.668162i	−0.995829	+	0.0912350i	$0.970919\pi$
$740$	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	0.916280	−	0.400538i	$-0.131177\pi$
$743$	−2.11279	−	7.88504i	−0.0775108	−	0.289274i	−0.993791	+	0.111264i	$0.964510\pi$
$744$	−8.14729			−0.298694
$745$	8.22545			0.301357
$746$	4.90345	+	18.2999i	0.179528	+	0.670008i
$747$	−6.48670	+	1.73811i	−0.237336	+	0.0635940i
$748$	45.1227	+	12.0906i	1.64985	+	0.442075i
$749$	−8.56596	+	26.0613i	−0.312993	+	0.952260i
$750$	−5.83086	−	10.0994i	−0.212913	−	0.368776i
$751$		−	5.56917i		−	0.203222i	−0.994824	−	0.101611i	$-0.967600\pi$
$751$		−	5.56917i		−	0.203222i	0.994824	−	0.101611i	$-0.0323997\pi$
$752$	−1.25120	−	0.335258i	−0.0456266	−	0.0122256i
$753$	−17.9352	−	10.3549i	−0.653596	−	0.377354i
$754$	−10.5425	−	4.83894i	−0.383937	−	0.176224i
$755$			20.7190i			0.754040i
$756$	−0.826136	+	2.51346i	−0.0300463	+	0.0914138i
$757$	−15.2061	+	26.3377i	−0.552675	+	0.957262i	0.445405	+	0.895329i	$0.353060\pi$
$757$	−15.2061	+	26.3377i	−0.552675	+	0.957262i	−0.998080	+	0.0619325i	$0.980274\pi$
$758$	29.9662	+	17.3010i	1.08842	+	0.628400i
$759$	0.363342	−	0.0973572i	0.0131885	−	0.00353384i
$760$	−8.26176	+	8.26176i	−0.299685	+	0.299685i
$761$	1.25642	+	4.68902i	0.0455451	+	0.169977i	0.984952	−	0.172827i	$-0.0552901\pi$
$761$	1.25642	+	4.68902i	0.0455451	+	0.169977i	−0.939407	+	0.342804i	$0.888623\pi$
$762$	4.33060	−	4.33060i	0.156881	−	0.156881i
$763$	−37.1706	−	2.07484i	−1.34567	−	0.0751142i
$764$	−10.9386	−	6.31539i	−0.395744	−	0.228483i
$765$	8.02255	+	8.02255i	0.290056	+	0.290056i
$766$	11.6330	−	20.1489i	0.420316	−	0.728008i
$767$	−3.34349	−	35.7347i	−0.120727	−	1.29031i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	21.1806	−	5.67534i	0.763794	−	0.204658i	0.144166	−	0.989554i	$-0.453950\pi$
$769$	21.1806	−	5.67534i	0.763794	−	0.204658i	0.619628	+	0.784896i	$0.287283\pi$
$770$	1.38704	−	24.8487i	0.0499854	−	0.895487i
$771$	−8.23387	+	4.75383i	−0.296536	+	0.171205i
$772$	1.91757	+	0.513811i	0.0690149	+	0.0184925i
$773$	−1.87524	−	1.87524i	−0.0674477	−	0.0674477i	0.672578	−	0.740026i	$-0.265187\pi$
$773$	−1.87524	−	1.87524i	−0.0674477	−	0.0674477i	−0.740026	+	0.672578i	$0.765187\pi$
$774$	3.14106	+	3.14106i	0.112903	+	0.112903i
$775$	−21.3694	−	5.72592i	−0.767613	−	0.205681i
$776$	2.22075	−	1.28215i	0.0797203	−	0.0460266i
$777$	6.99711	−	10.6948i	0.251020	−	0.383673i
$778$	−19.4286	+	5.20589i	−0.696550	+	0.186640i
$779$	26.6696	−	15.3977i	0.955537	−	0.551680i
$780$	−2.27335	+	4.95293i	−0.0813990	+	0.177343i
$781$	1.60268	−	2.77592i	0.0573483	−	0.0993301i
$782$	0.320814	+	0.320814i	0.0114723	+	0.0114723i
$783$	−2.78623	−	1.60863i	−0.0995719	−	0.0574879i
$784$	5.63500	+	4.15293i	0.201250	+	0.148319i
$785$	−23.8542	+	23.8542i	−0.851393	+	0.851393i
$786$	2.98939	+	11.1566i	0.106628	+	0.397941i
$787$	−9.45383	+	9.45383i	−0.336992	+	0.336992i	−0.855234	−	0.518242i	$-0.826587\pi$
$787$	−9.45383	+	9.45383i	−0.336992	+	0.336992i	0.518242	+	0.855234i	$0.326587\pi$
$788$	−3.47158	+	0.930208i	−0.123670	+	0.0331373i
$789$	−15.4395	−	8.91400i	−0.549661	−	0.317347i
$790$	−8.66741	+	15.0124i	−0.308373	+	0.534117i
$791$	−28.6226	+	5.98223i	−1.01770	+	0.212704i
$792$			6.22339i			0.221139i
$793$	−2.80330	+	1.03949i	−0.0995480	+	0.0369134i
$794$	−13.1120	−	7.57020i	−0.465327	−	0.268657i
$795$	−5.30344	−	1.42105i	−0.188094	−	0.0503995i
$796$		−	10.1883i		−	0.361116i
$797$	26.2340	+	45.4387i	0.929257	+	1.60952i	0.784568	+	0.620043i	$0.212885\pi$
$797$	26.2340	+	45.4387i	0.929257	+	1.60952i	0.144689	+	0.989477i	$0.453782\pi$
$798$	19.4293	+	6.38610i	0.687788	+	0.226065i
$799$	9.39183	+	2.51653i	0.332259	+	0.0890286i
$800$	2.62289	−	0.702801i	0.0927331	−	0.0248478i
$801$	0.742873	+	2.77244i	0.0262481	+	0.0979593i
$802$	18.9426			0.668886
$803$	−50.7285			−1.79017
$804$	−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
$808$	−2.08511	+	7.78173i	−0.0733539	+	0.273760i
$809$	2.72724	+	4.72372i	0.0958846	+	0.166077i	0.909977	−	0.414658i	$-0.136099\pi$
$809$	2.72724	+	4.72372i	0.0958846	+	0.166077i	−0.814093	+	0.580735i	$0.802765\pi$
$810$	−0.755742	+	1.30898i	−0.0265541	+	0.0459930i
$811$	−19.6603	−	19.6603i	−0.690367	−	0.690367i	0.271945	−	0.962313i	$-0.412333\pi$
$811$	−19.6603	−	19.6603i	−0.690367	−	0.690367i	−0.962313	+	0.271945i	$0.912333\pi$
$812$	−6.34505	+	5.67415i	−0.222668	+	0.199124i
$813$	−4.40116	+	16.4254i	−0.154355	+	0.576062i
$814$	7.78069	−	29.0379i	0.272713	−	1.01778i
$815$			17.8462i			0.625127i
$816$	−6.50061	+	3.75313i	−0.227567	+	0.131386i
$817$	24.2806	−	24.2806i	0.849472	−	0.849472i
$818$	−27.1980			−0.950956
$819$	9.53267	−	0.357941i	0.333099	−	0.0125075i
$820$	6.02152			0.210280
$821$	27.6149	−	27.6149i	0.963766	−	0.963766i	−0.0356006	−	0.999366i	$-0.511334\pi$
$821$	27.6149	−	27.6149i	0.963766	−	0.963766i	0.999366	+	0.0356006i	$0.0113344\pi$
$822$	3.67658	−	2.12267i	0.128235	−	0.0740368i
$823$			40.7030i			1.41882i	0.704798	+	0.709408i	$0.251038\pi$
$823$			40.7030i			1.41882i	−0.704798	+	0.709408i	$0.748962\pi$
$824$	3.58574	−	13.3822i	0.124915	−	0.466190i
$825$	−4.37381	+	16.3233i	−0.152276	+	0.568303i
$826$	−25.0198	−	8.22363i	−0.870551	−	0.286137i
$827$	36.0061	+	36.0061i	1.25205	+	1.25205i	0.954797	+	0.297257i	$0.0960718\pi$
$827$	36.0061	+	36.0061i	1.25205	+	1.25205i	0.297257	+	0.954797i	$0.403928\pi$
$828$	−0.0302214	+	0.0523450i	−0.00105027	+	0.00181911i
$829$	13.2122	+	22.8843i	0.458880	+	0.794804i	0.998902	−	0.0468470i	$-0.0149173\pi$
$829$	13.2122	+	22.8843i	0.458880	+	0.794804i	−0.540022	+	0.841651i	$0.681584\pi$
$830$	−2.62712	+	9.80454i	−0.0911887	+	0.340321i
$831$	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
$835$	13.4979			0.467113
$836$	48.1073			1.66383
$837$	2.10867	+	7.86967i	0.0728864	+	0.272016i
$838$	−7.06845	+	1.89398i	−0.244175	+	0.0654266i
$839$	−17.7480	−	4.75557i	−0.612731	−	0.164181i	−0.0609097	−	0.998143i	$-0.519400\pi$
$839$	−17.7480	−	4.75557i	−0.612731	−	0.164181i	−0.551821	+	0.833963i	$0.686067\pi$
$840$	2.66574	+	2.98093i	0.0919767	+	0.102852i
$841$	9.32460	+	16.1507i	0.321538	+	0.556920i
$842$		−	20.0851i		−	0.692178i
$843$	14.5118	+	3.88841i	0.499811	+	0.133924i
$844$	−22.0172	−	12.7116i	−0.757863	−	0.437552i
$845$	19.5937	+	1.47651i	0.674045	+	0.0507936i
$846$			1.29534i			0.0445346i
$847$	−54.6900	+	48.9073i	−1.87917	+	1.68047i
$848$	1.81627	−	3.14587i	0.0623709	−	0.108030i
$849$	10.4716	+	6.04580i	0.359386	+	0.207491i
$850$	−19.6881	+	5.27541i	−0.675296	+	0.180945i
$851$	0.206454	−	0.206454i	0.00707717	−	0.00707717i
$852$	0.133304	+	0.497499i	0.00456694	+	0.0170440i
$853$	−11.0707	+	11.0707i	−0.379055	+	0.379055i	−0.870761	−	0.491706i	$-0.836373\pi$
$853$	−11.0707	+	11.0707i	−0.379055	+	0.379055i	0.491706	+	0.870761i	$0.336373\pi$
$854$	−0.122273	+	2.19052i	−0.00418410	+	0.0749579i
$855$	10.1185	+	5.84194i	0.346047	+	0.199790i
$856$	−7.33177	−	7.33177i	−0.250595	−	0.250595i
$857$	18.8859	−	32.7113i	0.645128	−	1.11740i	−0.339143	−	0.940735i	$-0.610137\pi$
$857$	18.8859	−	32.7113i	0.645128	−	1.11740i	0.984272	−	0.176661i	$-0.0565295\pi$
$858$	21.0389	−	7.80143i	0.718257	−	0.266337i
$859$	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
$861$	−4.75320	−	9.40766i	−0.161989	−	0.320612i
$862$	2.72486	−	1.57320i	0.0928090	−	0.0535833i
$863$	4.93461	+	1.32222i	0.167976	+	0.0450090i	0.341827	−	0.939763i	$-0.388954\pi$
$863$	4.93461	+	1.32222i	0.167976	+	0.0450090i	−0.173851	+	0.984772i	$0.555621\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−23.6880	−	23.6880i	−0.805417	−	0.805417i
$866$	−1.13351	−	0.303724i	−0.0385184	−	0.0103210i
$867$	34.0729	−	19.6720i	1.15718	−	0.668095i
$868$	21.5222	+	1.20135i	0.730511	+	0.0407766i
$869$	68.9425	−	18.4731i	2.33871	−	0.626656i
$870$	−4.21135	+	2.43142i	−0.142778	+	0.0824330i
$871$	−2.55983	+	1.81550i	−0.0867367	+	0.0615160i
$872$	7.03553	−	12.1859i	0.238253	−	0.412666i
$873$	−1.81324	−	1.81324i	−0.0613687	−	0.0613687i
$874$	0.404631	+	0.233614i	0.0136868	+	0.00790210i
$875$	13.9138	+	27.5386i	0.470374	+	0.930976i
$876$	5.76381	−	5.76381i	0.194741	−	0.194741i
$877$	8.71418	+	32.5218i	0.294257	+	1.09818i	0.941806	+	0.336158i	$0.109128\pi$
$877$	8.71418	+	32.5218i	0.294257	+	1.09818i	−0.647548	+	0.762024i	$0.724206\pi$
$878$	19.8027	−	19.8027i	0.668310	−	0.668310i
$879$	7.51103	−	2.01257i	0.253341	−	0.0678824i
$880$	8.14632	+	4.70328i	0.274612	+	0.158548i
$881$	24.8501	−	43.0417i	0.837223	−	1.45011i	−0.0549851	−	0.998487i	$-0.517511\pi$
$881$	24.8501	−	43.0417i	0.837223	−	1.45011i	0.892208	−	0.451625i	$-0.149156\pi$
$882$	2.55298	−	6.51785i	0.0859632	−	0.219467i
$883$		−	3.25270i		−	0.109462i	−0.998501	−	0.0547310i	$-0.982570\pi$
$883$		−	3.25270i		−	0.109462i	0.998501	−	0.0547310i	$-0.0174301\pi$
$884$	20.8368	+	17.2713i	0.700819	+	0.580896i
$885$	−13.0300	−	7.52290i	−0.438000	−	0.252880i
$886$	14.0578	+	3.76678i	0.472282	+	0.126548i
$887$			29.9290i			1.00492i	0.864601	+	0.502459i	$0.167571\pi$
$887$			29.9290i			1.00492i	−0.864601	+	0.502459i	$0.832429\pi$
$888$	2.41526	+	4.18336i	0.0810509	+	0.140384i
$889$	−12.0784	+	10.8013i	−0.405098	+	0.362264i
$890$	4.19050	+	1.12284i	0.140466	+	0.0376377i
$891$	6.01134	−	1.61073i	0.201387	−	0.0539616i
$892$	−2.75865	−	10.2954i	−0.0923664	−	0.344716i
$893$	10.0131			0.335074
$894$	5.44197			0.182007
$895$	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
$899$	−6.78416	+	25.3188i	−0.226264	+	0.844430i
$900$	−1.35771	−	2.35162i	−0.0452569	−	0.0783873i
$901$	−13.6334	+	23.6137i	−0.454194	+	0.786687i
$902$	−17.5313	−	17.5313i	−0.583729	−	0.583729i
$903$	−7.83439	−	8.76072i	−0.260712	−	0.291538i
$904$	2.86049	−	10.6755i	0.0951384	−	0.355061i
$905$	4.42722	−	16.5226i	0.147166	−	0.549231i
$906$			13.7077i			0.455408i
$907$	−35.5773	+	20.5406i	−1.18133	+	0.682039i	−0.956321	−	0.292319i	$-0.905573\pi$
$907$	−35.5773	+	20.5406i	−1.18133	+	0.682039i	−0.225005	+	0.974358i	$0.572240\pi$
$908$	1.87977	−	1.87977i	0.0623823	−	0.0623823i
$909$	8.05624			0.267209
$910$	6.73571	−	12.7486i	0.223286	−	0.422613i
$911$	42.9297			1.42232			0.711162	−	0.703028i	$-0.248169\pi$
$911$	42.9297			1.42232			0.711162	+	0.703028i	$0.248169\pi$
$912$	−5.46599	+	5.46599i	−0.180997	+	0.180997i
$913$	36.1941	−	20.8967i	1.19785	−	0.691579i
$914$			23.4788i			0.776610i
$915$	−0.324394	+	1.21065i	−0.0107241	+	0.0400230i
$916$	0.650085	−	2.42615i	0.0214794	−	0.0801622i
$917$	−6.25180	−	29.9124i	−0.206453	−	0.987794i
$918$	5.30773	+	5.30773i	0.175181	+	0.175181i
$919$	−20.2343	+	35.0468i	−0.667466	+	1.15609i	0.311144	+	0.950363i	$0.399288\pi$
$919$	−20.2343	+	35.0468i	−0.667466	+	1.15609i	−0.978610	+	0.205723i	$0.934045\pi$
$920$	0.0456792	+	0.0791186i	0.00150600	+	0.00260846i
$921$	0.318474	−	1.18856i	0.0104941	−	0.0391644i
$922$	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
$926$	21.4120			0.703641
$927$	−13.8542			−0.455033
$928$	−0.832690	−	3.10764i	−0.0273344	−	0.102013i
$929$	−41.2398	+	11.0502i	−1.35303	+	0.362545i	−0.861254	−	0.508175i	$-0.830320\pi$
$929$	−41.2398	+	11.0502i	−1.35303	+	0.362545i	−0.491781	+	0.870719i	$0.663654\pi$
$930$	11.8949	+	3.18723i	0.390049	+	0.104513i
$931$	−50.3834	−	19.7347i	−1.65125	−	0.646778i
$932$	10.2191	+	17.7000i	0.334738	+	0.579783i
$933$		−	17.9561i		−	0.587858i
$934$	−27.9915	−	7.50030i	−0.915910	−	0.245417i
$935$	−61.1484	−	35.3041i	−1.99977	−	1.15457i
$936$	−1.50405	+	3.27686i	−0.0491615	+	0.107108i
$937$		−	20.8141i		−	0.679967i	−0.940431	−	0.339984i	$-0.889578\pi$
$937$		−	20.8141i		−	0.679967i	0.940431	−	0.339984i	$-0.110422\pi$
$938$	0.471128	+	2.25416i	0.0153829	+	0.0736010i
$939$	0.232688	−	0.403027i	0.00759347	−	0.0131523i
$940$	1.69558	+	0.978941i	0.0553036	+	0.0319295i
$941$	14.3586	−	3.84739i	0.468078	−	0.125421i	−0.0170677	−	0.999854i	$-0.505433\pi$
$941$	14.3586	−	3.84739i	0.468078	−	0.125421i	0.485146	+	0.874433i	$0.338766\pi$
$942$	−15.7820	+	15.7820i	−0.514204	+	0.514204i
$943$	−0.0623222	−	0.232590i	−0.00202949	−	0.00757416i
$944$	7.03877	−	7.03877i	0.229092	−	0.229092i
$945$	2.18941	−	3.34643i	0.0712216	−	0.108859i
$946$	−23.9414	−	13.8226i	−0.778402	−	0.449411i
$947$	−7.71031	−	7.71031i	−0.250551	−	0.250551i	0.570645	−	0.821197i	$-0.306693\pi$
$947$	−7.71031	−	7.71031i	−0.250551	−	0.250551i	−0.821197	+	0.570645i	$0.806693\pi$
$948$	−5.73437	+	9.93222i	−0.186244	+	0.322584i
$949$	−26.7106	−	12.2599i	−0.867062	−	0.397974i
$950$	−18.1782	+	10.4952i	−0.589778	+	0.340509i
$951$	0.157858	−	0.0422978i	0.00511889	−	0.00137160i
$952$	17.7257	−	8.95587i	0.574493	−	0.290262i
$953$	−2.68793	+	1.55188i	−0.0870707	+	0.0502703i	−0.542903	−	0.839795i	$-0.682675\pi$
$953$	−2.68793	+	1.55188i	−0.0870707	+	0.0502703i	0.455832	+	0.890066i	$0.349342\pi$
$954$	−3.50876	−	0.940170i	−0.113600	−	0.0304391i
$955$	13.4995	+	13.4995i	0.436835	+	0.436835i
$956$	12.0931	+	12.0931i	0.391118	+	0.391118i
$957$	19.3401	+	5.18216i	0.625176	+	0.167515i
$958$	25.4257	−	14.6796i	0.821468	−	0.474275i
$959$	−10.0252	+	5.06521i	−0.323730	+	0.163564i
$960$	−1.45998	+	0.391201i	−0.0471207	+	0.0126260i
$961$	30.6385	−	17.6891i	0.988338	−	0.570617i
$962$	11.1146	−	13.4092i	0.358351	−	0.432330i
$963$	−5.18435	+	8.97955i	−0.167063	+	0.289362i
$964$	−4.75087	−	4.75087i	−0.153015	−	0.153015i
$965$	−2.59861	−	1.50031i	−0.0836524	−	0.0482967i
$966$	0.0875525	−	0.133820i	0.00281696	−	0.00430560i
$967$	−22.1771	+	22.1771i	−0.713169	+	0.713169i	−0.967197	−	0.254028i	$-0.918244\pi$
$967$	−22.1771	+	22.1771i	−0.713169	+	0.713169i	0.254028	+	0.967197i	$0.418244\pi$
$968$	−7.17721	−	26.7857i	−0.230684	−	0.860926i
$969$	41.0291	−	41.0291i	1.31805	−	1.31805i
$970$	−3.74384	+	1.00316i	−0.120207	+	0.0322095i
$971$	−25.5522	−	14.7526i	−0.820010	−	0.473433i	0.0304098	−	0.999538i	$-0.490319\pi$
$971$	−25.5522	−	14.7526i	−0.820010	−	0.473433i	−0.850420	+	0.526104i	$0.823652\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	4.71538	+	22.5612i	0.151168	+	0.723279i
$974$			28.7439i			0.921013i
$975$	−6.24795	+	7.53780i	−0.200094	+	0.241403i
$976$	−0.718131	−	0.414613i	−0.0229868	−	0.0132714i
$977$	−1.02628	−	0.274992i	−0.0328338	−	0.00879778i	0.242365	−	0.970185i	$-0.422077\pi$
$977$	−1.02628	−	0.274992i	−0.0328338	−	0.00879778i	−0.275199	+	0.961387i	$0.588744\pi$
$978$			11.8071i			0.377549i
$979$	−8.93132	−	15.4695i	−0.285446	−	0.494407i
$980$	−6.60236	−	8.26761i	−0.210905	−	0.264099i
$981$	−13.5916	−	3.64186i	−0.433946	−	0.116276i
$982$	−30.9903	+	8.30381i	−0.988939	+	0.264985i
$983$	1.80054	+	6.71970i	0.0574282	+	0.214325i	0.988677	−	0.150059i	$-0.0479463\pi$
$983$	1.80054	+	6.71970i	0.0574282	+	0.214325i	−0.931249	+	0.364384i	$0.881280\pi$
$984$	3.98384			0.127000
$985$	5.43235			0.173089
$986$	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
$990$	2.43460	−	9.08604i	0.0773766	−	0.288773i
$991$	9.41029	+	16.2991i	0.298928	+	0.517758i	0.975891	−	0.218259i	$-0.0700378\pi$
$991$	9.41029	+	16.2991i	0.298928	+	0.517758i	−0.676963	+	0.736017i	$0.736704\pi$
$992$	−4.07364	+	7.05576i	−0.129338	+	0.224020i
$993$	−8.31583	−	8.31583i	−0.263895	−	0.263895i
$994$	−0.278784	−	1.33387i	−0.00884249	−	0.0423078i
$995$	−3.98568	+	14.8748i	−0.126355	+	0.471562i
$996$	−1.73811	+	6.48670i	−0.0550740	+	0.205539i
$997$			5.74478i			0.181939i	0.995854	+	0.0909694i	$0.0289966\pi$
$997$			5.74478i			0.181939i	−0.995854	+	0.0909694i	$0.971003\pi$
$998$	2.88405	−	1.66510i	0.0912929	−	0.0527080i
$999$	3.41570	−	3.41570i	0.108068	−	0.108068i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.8	✓	40	7.5	odd	6
546.2.by.b.115.8	yes	40	13.11	odd	12
546.2.cg.b.271.3	yes	40	91.89	even	12	inner
546.2.cg.b.409.3	yes	40	1.1	even	1	trivial

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.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.391201 + 1.45998i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.826136 - 2.51346i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.391201 + 1.45998i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.826136 - 2.51346i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.755742 - 1.30898i) q^{10} +(-1.61073 + 6.01134i) 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} -1.00000 q^{16} +7.50626 q^{17} +(0.258819 + 0.965926i) q^{18} +(7.46668 - 2.00069i) q^{19} +(1.45998 + 0.391201i) q^{20} +(-0.541277 - 2.58979i) q^{21} +(-3.11170 - 5.38962i) q^{22} -0.0604428i q^{23} +(0.965926 + 0.258819i) q^{24} +(2.35162 + 1.35771i) q^{25} +(-0.335884 - 3.58987i) q^{26} -1.00000i q^{27} +(-2.51346 - 0.826136i) q^{28} +(1.60863 - 2.78623i) q^{29} +(-1.30898 - 0.755742i) q^{30} +(-7.86967 + 2.10867i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.61073 + 6.01134i) q^{33} +(-5.30773 + 5.30773i) q^{34} +(3.34643 + 2.18941i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(3.41570 + 3.41570i) q^{37} +(-3.86504 + 6.69444i) q^{38} +(-0.604689 + 3.55448i) q^{39} +(-1.30898 + 0.755742i) q^{40} +(3.84810 - 1.03109i) q^{41} +(2.21400 + 1.44852i) q^{42} +(3.84700 - 2.22107i) q^{43} +(6.01134 + 1.61073i) q^{44} +(1.06878 + 1.06878i) q^{45} +(0.0427395 + 0.0427395i) q^{46} +(1.25120 + 0.335258i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-5.63500 - 4.15293i) q^{49} +(-2.62289 + 0.702801i) q^{50} +(6.50061 - 3.75313i) q^{51} +(2.77593 + 2.30092i) q^{52} +(-1.81627 + 3.14587i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-8.14632 - 4.70328i) q^{55} +(2.36145 - 1.19312i) q^{56} +(5.46599 - 5.46599i) q^{57} +(0.832690 + 3.10764i) q^{58} +(-7.03877 + 7.03877i) q^{59} +(1.45998 - 0.391201i) q^{60} +(0.718131 + 0.414613i) q^{61} +(4.07364 - 7.05576i) q^{62} +(-1.76365 - 1.97219i) q^{63} +1.00000i q^{64} +(-3.15268 - 4.44524i) q^{65} +(-5.38962 - 3.11170i) q^{66} +(0.840744 + 0.225277i) q^{67} -7.50626i q^{68} +(-0.0302214 - 0.0523450i) q^{69} +(-3.91443 + 0.818131i) q^{70} +(-0.497499 - 0.133304i) q^{71} +(0.965926 - 0.258819i) q^{72} +(2.10970 + 7.87352i) q^{73} -4.83053 q^{74} +2.71542 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} +(0.391201 - 1.45998i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.99192 + 3.45011i) q^{82} +(-4.74859 - 4.74859i) q^{83} +(-2.58979 + 0.541277i) q^{84} +(-2.93646 + 10.9590i) q^{85} +(-1.14971 + 4.29077i) q^{86} -3.21727i q^{87} +(-5.38962 + 3.11170i) q^{88} +(-2.02957 + 2.02957i) q^{89} -1.51148 q^{90} +(5.07632 + 8.07657i) q^{91} -0.0604428 q^{92} +(-5.76100 + 5.76100i) q^{93} +(-1.12180 + 0.647669i) q^{94} +11.6839i q^{95} +(0.258819 - 0.965926i) q^{96} +(0.663690 - 2.47693i) q^{97} +(6.92111 - 1.04798i) q^{98} +(4.40060 + 4.40060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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